ratios and proportions

Question

The sides of a rectangle are in the ratio 2:5. The perimeter of the rectangle is 70 cm. What is the width of the rectangle?

Answer 1

Length = 10 cm

Width = 25 cm

For a rectangle Perimeter = 2Length + 2Width = 2L + 2W

And L/W = 2/5

We have

70 = 2L + 2W

So if we divide both sides of the equation by 2

35 = L + W

L/W = 2/5

We can set up a proportion to find the sides

L/W = 2/5 has a total of L + W = 2 + 5 = 7

Comparing totals to totals we can

5/7 = W/35

Cross products gives

5(35)/7 = W

25 = W

We can do the same for the L

2/7 = L/35

2(35)/7 = L

10 = L

We can check as follows:

Perimeter = 70 = 2(10) + 2(25) = 20 + 50 = 70

And L/W = 2/5 = 10/25 = 2/5

I hope you find this useful and send me a message if you have any questions.