Perimeter Word Problems

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Question 1 of 5

1. Question
An athlete runs a particular route during his training session which is shown in the shape below. How long is one lap?
- (15)km
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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 $1$ $1$ lap) $=$ $=$ $2 + 1 + 4 + 5 + 3$ $2+1+4+5+3$

$=$ $=$ $15$ $15$ km

The athlete runs $15$ $15$ km in one lap.

$15$ $15$ km
Question 2 of 5

2. Question
Find the cost of fencing the rectangular field shown below if the cost of fencing is $$ 5$ $$5$ per metre.
- $$$ $$$ (2150)
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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 $=$ $=$ $62 + 62 + 153 + 153$ $62+62+153+153$

$=$ $=$ $430$ $430$ m

Finally, multiply the perimeter by the fencing cost per metre.

Cost per metre = $$ 5$ $$5$

Total fencing cost $=$ $=$ $430 \times 5$ $430xx5$

$=$ $=$ $$ 2150$ $$2150$

The cost of fencing the rectangular field is $$ 2150$ $$2150$ .

$$ 2150$ $$2150$
Question 3 of 5

3. Question
Find the cost of fencing this square piece of land if the cost of fencing is $$ 20$ $$20$ per metre.
- $$$ $$$ (3800)
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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 $=$ $=$ $47.5 + 47.5 + 47.5 + 47.5$ $47.5+47.5+47.5+47.5$

$=$ $=$ $190$ $190$ m

Finally, multiply the perimeter by the fencing cost per metre.

Cost per metre = $$ 20$ $$20$

Total fencing cost $=$ $=$ $190 \times 20$ $190xx20$

$=$ $=$ $$ 3800$ $$3800$

The cost of fencing the square piece of land is $$ 3800$ $$3800$ .

$$ 3800$ $$3800$
Question 4 of 5

4. Question
Find the length of a side of this square given its perimeter.
- (9)cm
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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 $4$ $4$ sides, we can divide its perimeter by $4$ $4$ to get the length of each side.

$P = 36$ $P=36$ cm

Length $=$ $=$ $36 \div 4$ $36-:4$

$=$ $=$ $9$ $9$ cm

Check our work

To confirm the answer, find the perimeter of a square with each side measuring $9$ $9$ cm

Do this by adding all $4$ $4$ sides of the square.

$P$ $P$ $=$ $=$ $9 + 9 + 9 + 9$ $9+9+9+9$

$=$ $=$ $36$ $36$ cm

Since the result is the same as the given perimeter, the answer is correct

$9$ $9$ cm

Question 5 of 5

A rectangular roof has a length of

12

$12$ m and a perimeter of

38

$38$ m. What is the width of the roof?

(7)m

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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.

L = 12

$L=12$ m

P = 38

$P=38$ m

W = ?

$W=?$

Knowing that Perimeter is the sum of all sides of a shape, we can form an equation using the values given.

$P$ $P$	$=$ $=$	$L + L + W + W$ $L+L+W+W$
$38$ $38$	$=$ $=$	$12 + 12 + W + W$ $12+12+W+W$	Substitute known values
$38$ $38$	$=$ $=$	$24 + 2 W$ $24+2W$	Simplify
$38$ $38$ $- 24$ $-24$	$=$ $=$	$24 + 2 W$ $24+2W$ $- 24$ $-24$	Subtract $24$ $24$ from both sides
$14$ $14$	$=$ $=$	$2 W$ $2W$
$14$ $14$ $\div 2$ $-:2$	$=$ $=$	$2 W$ $2W$ $\div 2$ $-:2$	Divide both sides by $2$ $2$
$7$ $7$	$=$ $=$	$W$ $W$
$W$ $W$	$=$ $=$	$7$ $7$ m

Therefore, the width of the roof is

7

$7$ m

7

$7$ m

Perimeter Word Problems

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Quiz summary

Information

1. Question

Hint

Exceptional!

2. Question

Hint

Well Done!

3. Question

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Excellent!

4. Question

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Fantastic!

5. Question

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Exceptional!

Quizzes

Perimeter (total distance of $1$ $1$ lap)	$=$ $=$	$2 + 1 + 4 + 5 + 3$ $2+1+4+5+3$
	$=$ $=$	$15$ $15$ km

Perimeter	$=$ $=$	$62 + 62 + 153 + 153$ $62+62+153+153$
	$=$ $=$	$430$ $430$ m

Total fencing cost	$=$ $=$	$430 \times 5$ $430xx5$
	$=$ $=$	$$ 2150$ $$2150$

Perimeter	$=$ $=$	$47.5 + 47.5 + 47.5 + 47.5$ $47.5+47.5+47.5+47.5$
	$=$ $=$	$190$ $190$ m

Total fencing cost	$=$ $=$	$190 \times 20$ $190xx20$
	$=$ $=$	$$ 3800$ $$3800$

Length	$=$ $=$	$36 \div 4$ $36-:4$
	$=$ $=$	$9$ $9$ cm