Equation Problems (Perimeter)

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Question 1 of 3

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

$P=44$ cm

Side $1=x$ cm

Side $2=(x+6)$ cm

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

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

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

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

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

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

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

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

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

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

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

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

$5$ $x$ $divide5$ $=$ $40$ $divide5$

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

$x=8$
Question 2 of 3

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

Equal Side $2=x$

Base $=(x-5)$

$P=55$ cm

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

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

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

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

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

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

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

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

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

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

$3$ $x$ $divide3$ $=$ $60$ $divide3$

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

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

Equal Side $1$ $=$ $x$

$=$ $20$ cm

Equal Side $2$ $=$ $x$

$=$ $20$ cm

Base $=$ $x$ $-5$

$=$ $20$ $-5$

$=$ $15$ cm

Check our work

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

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

$55$ $=$ $55$

Since the equation is true, the answer is correct.

Equal Side $1=20$ cm

Equal Side $2=20$ cm

Base $=15$ cm
Question 3 of 3

3. Question
A rectangle is twice as long as it is wide. The total perimeter is $126$ cm. What are the dimensions of this rectangle?
- Length $=$ (42)cm
  
  Width $=$ (21) cm
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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 $w$ , the length should be $2w$

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

$P=126$ cm

Side $1$ and $2=w$ cm

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

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

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

$126$ $=$ $6w$ Simplify

$6w$ $=$ $126$

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

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

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

$6$ $w$ $divide6$ $=$ $126$ $divide6$

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

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

Length $=$ $2$ $w$

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

$=$ $42$ cm

Width $=$ $w$

$=$ $21$ cm

Length $=42$ cm

Width $=21$ cm

Equation Problems (Perimeter)

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Quiz summary

Information

1. Question

Hint

Fantastic!

Inverse Operations

2. Question

Hint

Good Job!

Inverse Operations

3. Question

Hint

Excellent!

Inverse Operations

Quizzes

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

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

$5$ $x$	$=$	$40$
$5$ $x$ $divide5$	$=$	$40$ $divide5$
$x$	$=$	$8$	$5divide5$ cancels out

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

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

$3$ $x$	$=$	$60$
$3$ $x$ $divide3$	$=$	$60$ $divide3$
$x$	$=$	$20$	$3divide3$ cancels out

$P$	$=$	Side $1$ $+$ Side $2$ $+$ Side $3$ $+$ Side $4$
$126$	$=$	$w$ $+$ $w$ $+$ $2w$ $+$ $2w$	Substitute the values
$126$	$=$	$6w$	Simplify
$6w$	$=$	$126$

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

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