Equation Problems (Perimeter)

Years

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 3

1. Question
Find $x$ $x$ if the perimeter of the triangle below is $44$ $44$ cm.
- $x =$ $x=$ (8)
Hint

Help Video
Correct

Fantastic!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Inverse Operations

When moving a term to the other side of an equation, the operation is inversed.

First, form an equation knowing that the Perimeter of a shape is the sum of all sides.

$P = 44$ $P=44$ cm

Side $1 = x$ $1=x$ cm

Side $2 = (x + 6)$ $2=(x+6)$ cm

Side $3 = (3 x - 2)$ $3=(3x-2)$ cm

$P$ $P$ $=$ $=$ Side $1$ $1$ $+$ $+$ Side $2$ $2$ $+$ $+$ Side $3$ $3$

$44$ $44$ $=$ $=$ $x$ $x$ $+$ $+$ $(x + 6)$ $(x+6)$ $+$ $+$ $(3 x - 2)$ $(3x-2)$ Substitute the values

$44$ $44$ $=$ $=$ $5 x + 4$ $5x+4$ Simplify

$5 x + 4$ $5x+4$ $=$ $=$ $44$ $44$

To solve for $x$ $x$ , it needs to be alone on one side.

Start by moving $4$ $4$ to the other side by subtracting $4$ $4$ from both sides of the equation.

$5$ $5$ $x$ $x$ $+ 4$ $+4$ $=$ $=$ $44$ $44$

$5$ $5$ $x$ $x$ $+ 4$ $+4$ $- 4$ $-4$ $=$ $=$ $44$ $44$ $- 4$ $-4$

$5$ $5$ $x$ $x$ $=$ $=$ $40$ $40$ $4 - 4$ $4-4$ cancels out

Finally, remove $5$ $5$ by dividing both sides of the equation by $5$ $5$ .

$5$ $5$ $x$ $x$ $=$ $=$ $40$ $40$

$5$ $5$ $x$ $x$ $\div 5$ $divide5$ $=$ $=$ $40$ $40$ $\div 5$ $divide5$

$x$ $x$ $=$ $=$ $8$ $8$ $5 \div 5$ $5divide5$ cancels out

$x = 8$ $x=8$
Question 2 of 3

2. Question
An isosceles triangle has a perimeter of $55$ $55$ cm and a base that is $5$ $5$ cm less than either of the other $2$ $2$ equal sides. What are the lengths of all three sides?
- Equal Side $1 =$ $1=$ (20)cm
  
  Equal Side $2 =$ $2=$ (20)cm
  
  Base $=$ $=$ (15)cm
Hint

Help Video
Correct

Good Job!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Inverse Operations

When moving a term to the other side of an equation, the operation is inversed.

First, label the values and form an equation knowing that the Perimeter of a shape is the sum of all sides.

Equal Side $1 = x$ $1=x$

Equal Side $2 = x$ $2=x$

Base $= (x - 5)$ $=(x-5)$

$P = 55$ $P=55$ cm

Equal Side $1$ $1$ $+$ $+$ Equal Side $2$ $2$ $+$ $+$ Base $=$ $=$ $P$ $P$

$x$ $x$ $+$ $+$ $x$ $x$ $+$ $+$ $x - 5$ $x-5$ $=$ $=$ $55$ $55$ Substitute the values

$3 x - 5$ $3x-5$ $=$ $=$ $55$ $55$ Simplify

To solve for $x$ $x$ , it needs to be alone on one side.

Start by moving $5$ $5$ to the other side by adding $5$ $5$ to both sides of the equation.

$3$ $3$ $x$ $x$ $- 5$ $-5$ $=$ $=$ $55$ $55$

$3$ $3$ $x$ $x$ $- 5$ $-5$ $+ 5$ $+5$ $=$ $=$ $55$ $55$ $+ 5$ $+5$

$3$ $3$ $x$ $x$ $=$ $=$ $60$ $60$ $- 5 + 5$ $-5+5$ cancels out

Finally, remove $3$ $3$ by dividing both sides of the equation by $3$ $3$ .

$3$ $3$ $x$ $x$ $=$ $=$ $60$ $60$

$3$ $3$ $x$ $x$ $\div 3$ $divide3$ $=$ $=$ $60$ $60$ $\div 3$ $divide3$

$x$ $x$ $=$ $=$ $20$ $20$ $3 \div 3$ $3divide3$ cancels out

Substitute $x = 20$ $x=20$ to find each side length.

Equal Side $1$ $1$ $=$ $=$ $x$ $x$

$=$ $=$ $20$ $20$ cm

Equal Side $2$ $2$ $=$ $=$ $x$ $x$

$=$ $=$ $20$ $20$ cm

Base $=$ $=$ $x$ $x$ $- 5$ $-5$

$=$ $=$ $20$ $20$ $- 5$ $-5$

$=$ $=$ $15$ $15$ cm

Check our work

To confirm our answer, add the $3$ $3$ numbers and check if the sum is $55$ $55$ .

$20 + 20 + 15$ $20+20+15$ $=$ $=$ $55$ $55$

$55$ $55$ $=$ $=$ $55$ $55$

Since the equation is true, the answer is correct.

Equal Side $1 = 20$ $1=20$ cm

Equal Side $2 = 20$ $2=20$ cm

Base $= 15$ $=15$ cm
Question 3 of 3

3. Question
A rectangle is twice as long as it is wide. The total perimeter is $126$ $126$ cm. What are the dimensions of this rectangle?
- Length $=$ $=$ (42)cm
  
  Width $=$ $=$ (21) cm
Hint

Help Video
Correct

Excellent!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Inverse Operations

When moving a term to the other side of an equation, the operation is inversed.

First, draw a rectangle and label it using the given statement: “A rectangle is twice as long as it is wide.”

This means if the width is $w$ $w$ , the length should be $2 w$ $2w$

Form an equation knowing that the Perimeter of a shape is the sum of all sides.

$P = 126$ $P=126$ cm

Side $1$ $1$ and $2 = w$ $2=w$ cm

Side $3$ $3$ and $4 = 2 w$ $4=2w$ cm

$P$ $P$ $=$ $=$ Side $1$ $1$ $+$ $+$ Side $2$ $2$ $+$ $+$ Side $3$ $3$ $+$ $+$ Side $4$ $4$

$126$ $126$ $=$ $=$ $w$ $w$ $+$ $+$ $w$ $w$ $+$ $+$ $2 w$ $2w$ $+$ $+$ $2 w$ $2w$ Substitute the values

$126$ $126$ $=$ $=$ $6 w$ $6w$ Simplify

$6 w$ $6w$ $=$ $=$ $126$ $126$

Now, to solve for $w$ $w$ , it needs to be alone on one side.

Remove $6$ $6$ by dividing both sides of the equation by $6$ $6$ .

$6$ $6$ $w$ $w$ $=$ $=$ $126$ $126$

$6$ $6$ $w$ $w$ $\div 6$ $divide6$ $=$ $=$ $126$ $126$ $\div 6$ $divide6$

$w$ $w$ $=$ $=$ $21$ $21$ $6 \div 6$ $6divide6$ cancels out

Finally, substitute $w = 21$ $w=21$ to the dimensions of the rectangle.

Length $=$ $=$ $2$ $2$ $w$ $w$

$=$ $=$ $2 ($ $2($ $21$ $21$ $)$ $)$

$=$ $=$ $42$ $42$ cm

Width $=$ $=$ $w$ $w$

$=$ $=$ $21$ $21$ cm

Length $= 42$ $=42$ cm

Width $= 21$ $=21$ cm

Equation Problems (Perimeter)

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Fantastic!

Inverse Operations

2. Question

Hint

Good Job!

Inverse Operations

3. Question

Hint

Excellent!

Inverse Operations

Quizzes

$P$ $P$	$=$ $=$	Side $1$ $1$ $+$ $+$ Side $2$ $2$ $+$ $+$ Side $3$ $3$
$44$ $44$	$=$ $=$	$x$ $x$ $+$ $+$ $(x + 6)$ $(x+6)$ $+$ $+$ $(3 x - 2)$ $(3x-2)$	Substitute the values
$44$ $44$	$=$ $=$	$5 x + 4$ $5x+4$	Simplify
$5 x + 4$ $5x+4$	$=$ $=$	$44$ $44$

$5$ $5$ $x$ $x$ $+ 4$ $+4$	$=$ $=$	$44$ $44$
$5$ $5$ $x$ $x$ $+ 4$ $+4$ $- 4$ $-4$	$=$ $=$	$44$ $44$ $- 4$ $-4$
$5$ $5$ $x$ $x$	$=$ $=$	$40$ $40$	$4 - 4$ $4-4$ cancels out

Equal Side $1$ $1$ $+$ $+$ Equal Side $2$ $2$ $+$ $+$ Base	$=$ $=$	$P$ $P$
$x$ $x$ $+$ $+$ $x$ $x$ $+$ $+$ $x - 5$ $x-5$	$=$ $=$	$55$ $55$	Substitute the values
$3 x - 5$ $3x-5$	$=$ $=$	$55$ $55$	Simplify

$3$ $3$ $x$ $x$ $- 5$ $-5$	$=$ $=$	$55$ $55$
$3$ $3$ $x$ $x$ $- 5$ $-5$ $+ 5$ $+5$	$=$ $=$	$55$ $55$ $+ 5$ $+5$
$3$ $3$ $x$ $x$	$=$ $=$	$60$ $60$	$- 5 + 5$ $-5+5$ cancels out

Base	$=$ $=$	$x$ $x$ $- 5$ $-5$
	$=$ $=$	$20$ $20$ $- 5$ $-5$
	$=$ $=$	$15$ $15$ cm

$20 + 20 + 15$ $20+20+15$	$=$ $=$	$55$ $55$
$55$ $55$	$=$ $=$	$55$ $55$

$6$ $6$ $w$ $w$	$=$ $=$	$126$ $126$
$6$ $6$ $w$ $w$ $\div 6$ $divide6$	$=$ $=$	$126$ $126$ $\div 6$ $divide6$
$w$ $w$	$=$ $=$	$21$ $21$	$6 \div 6$ $6divide6$ cancels out

Length	$=$ $=$	$2$ $2$ $w$ $w$
	$=$ $=$	$2 ($ $2($ $21$ $21$ $)$ $)$
	$=$ $=$	$42$ $42$ cm