The area of a playground is 160 yd2. the width of the playground is 6 yd longer than its length. find the length and width of the playground.

Length of the playground is 10 yd and the Width of the playground is 16 yd .

Step-by-step explanation:

Formula

Area of a rectangle = Length × Width

As given

The area of a playground is 160 yd².

The width of the playground is 6 yd longer than its length.

Let us assume that the length be x .

Thus

Width = x + 6

Put all the values in the formula

160 = x × (x + 6)

160 = x² + 6x

x² + 6x - 160 = 0

x² + 16x - 10x - 160 = 0

x (x + 16)-10 (x + 16) = 0

(x -10)(x + 16) = 0

Thus

Either (x - 10) = 0 or (x + 16 ) = 0

x = 10 or x = -16

(Negative value is neglected because sides cannot be negative.)

Thus

x = 10

Length = 10 yd

Width = 10 + 6

             = 16 yd

Therefore the length of the playground is 10 yd and the width of the playground is 16 yd .

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