Question

the area of a playground is 20 square yards. The length of the playground is 5 times longer than its width. Find the length and width of the playground

Answer 1

The area of a rectangle = length x width so:
A = l x w

if we know the area of the playground is 20 sq yards, then:

20 = l x w

if the length is 5 times the width, then:
l = 5w

We can combine these equations by substituting this " l " into the first equation:

20 = 5w x w

Now solve!

20 = 5w x w
combine the w's
20 = 5w²
divide both sides by 5
4 = w²
square root both sides
2 = w

The width of the playground is 2 yards. 

To find the length of the playground, you can plug that back into the equation
l = 5w 
l = 5(2)
l = 10

The length of the playground is 10 yards.