A rectangular roof shingle has a perimeter of 32 inches and an area of 60 square inches. What are the dimensions of the shingle?

Length = 6 inches, Width = 10 inches

Step-by-step explanation:

A rectangular roof shingle has a perimeter of 32 inches and an area of 60 square inches. What are the dimensions of the shingle?

Note :

L = Length

W = Width

The perimeter of a rectangle = 2( L + W)

The area of a rectangle = LW.

A rectangular roof shingle has a perimeter of 32 inches and an area of 60 square inches.

32 = 2( L + W)

Divide both sides by 2

16 = L + W Equation 1

L = 16 - W

Also:

LW = 60 Equation 2

Let us substitute 16 - W for L in Equation 2

(16 - W)W = 60

16W - W² = 60

W² - 16W + 60 = 0

W² - 6W - 10W + 60 = 0

W(W - 6) - 10(W - 6) = 0

W - 6 = 0, W = 6 inches

W - 10 = 0, W = 10 inches

Solving for L

W = 10

L = 16 - 10

L = 6 inches

Therefore, the dimensions of the shingle =

Length = 6 inches, Width = 10 inches

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