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Question 1 of 2
The perimeter of the plot of land below is 98m
(i) What is the length and width of the land?
(ii) What is the area of the land?
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A word problem can be translated into an equation for easier solving.
(i) Find the length and width of the land.
Slot in the given values into the Perimeter Formula to form an equation
P |
= |
2l+2w |
Perimeter Formula |
98 |
= |
2(x+7)+2(x) |
98 |
= |
2(x+7)+2(x) |
98 |
= |
2x+14+2x |
98 |
= |
4x+14 |
4x+14 |
= |
98 |
4x+14 -14 |
= |
98 -14 |
Subtract 14 from both sides |
4x |
= |
84 |
4x÷4 |
= |
84÷4 |
Divide both sides by 4 |
x |
= |
21m |
width of the land |
|
|
x+7 |
|
= |
21+7 |
Substitute x |
|
= |
28m |
length of the land |
(ii) Find the area of the land.
Slot in the values from part (i) into the Area Formula
A |
= |
lw |
Area Formula |
|
= |
(28)(21) |
|
= |
588m2 |
(i) length: 28m, width: 21m
(ii) Area: 588m2
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Question 2 of 2
Find the size of each angle in this triangle:
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A word problem can be translated into an equation for easier solving.
Form an equation using the values given
Remember that the sum of all interior angles in a triangle is 180°
Angle 1: 3x
Angle 2: 3x+12
Angle 3: 4x-2
Angle 1+ Angle 2+ Angle 3 |
= |
180° |
3x+(3x+12)+(4x-2) |
= |
180° |
3x+(3x+12)+(4x-2) |
= |
180° |
10x+10 |
= |
180 |
10x+10 -10 |
= |
180 -10 |
Subtract 10 from both sides |
10x |
= |
170 |
10x÷10 |
= |
170÷10 |
Divide both sides by 10 |
x |
= |
17 |
Solve for the size of each angle
|
|
3x+12 |
|
= |
3(17)+12 |
|
= |
51+12 |
|
= |
63° |
|
|
4x-2 |
|
= |
4(17)-2 |
|
= |
68-2 |
|
= |
66° |
Angle 1: 51°
Angle 2: 63°
Angle 3: 66°