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Question 1 of 5
An athlete runs a particular route during his training session which is shown in the shape below. How long is one lap?
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The Perimeter of a shape is the sum of all the side lengths.
We can find the distance of one lap by solving for the perimeter of the route.
Since the side lengths are already given, add them all to find the perimeter.
| Perimeter (total distance of 1 lap) |
= |
2+1+4+5+3 |
|
= |
15 km |
The athlete runs 15 km in one lap.
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Question 2 of 5
Find the cost of fencing the rectangular field shown below if the cost of fencing is $5 per metre.
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The Perimeter of a shape is the sum of all the side lengths.
First, find the total distance that needs to be fenced by solving for the perimeter of the rectangle.
Start with finding the missing lengths.
Remember that opposite sides in a rectangle are equal.
Now that we know all the side lengths, add them all to find the perimeter.
| Perimeter |
= |
62+62+153+153 |
|
= |
430 m |
Finally, multiply the perimeter by the fencing cost per metre.
| Total fencing cost |
= |
430×5 |
|
= |
$2150 |
The cost of fencing the rectangular field is $2150.
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Question 3 of 5
Find the cost of fencing this square piece of land if the cost of fencing is $20 per metre.
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The Perimeter of a shape is the sum of all the side lengths.
First, find the total distance that needs to be fenced by solving for the perimeter of the square.
Add all lengths of the square.
| Perimeter |
= |
47.5+47.5+47.5+47.5 |
|
= |
190 m |
Finally, multiply the perimeter by the fencing cost per metre.
| Total fencing cost |
= |
190×20 |
|
= |
$3800 |
The cost of fencing the square piece of land is $3800.
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Question 4 of 5
Find the length of a side of this square given its perimeter.
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The Perimeter of a shape is the sum of all the side lengths.
All sides in a square are equal.
Since a square has 4 sides, we can divide its perimeter by 4 to get the length of each side.
Check our work
To confirm the answer, find the perimeter of a square with each side measuring 9 cm
Do this by adding all 4 sides of the square.
Since the result is the same as the given perimeter, the answer is correct
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Question 5 of 5
A rectangular roof has a length of 12m and a perimeter of 38m. What is the width of the roof?
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The Perimeter of a shape is the sum of all the side lengths.
First, label all the values and slot them into the diagram.
Remember that opposite sides of a rectangle are equal.
Knowing that Perimeter is the sum of all sides of a shape, we can form an equation using the values given.
| P |
= |
L+L+W+W |
| 38 |
= |
12+12+W+W |
Substitute known values |
| 38 |
= |
24+2W |
Simplify |
| 38 −24 |
= |
24+2W−24 |
Subtract 24 from both sides |
| 14 |
= |
2W |
| 14÷2 |
= |
2W÷2 |
Divide both sides by 2 |
| 7 |
= |
W |
| W |
= |
7 m |
Therefore, the width of the roof is 7 m
