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3 years ago

The length of a rectangle is 8feet less than the width. The perimeter is 64 feet. Find the length and the width

Mathematics

1 answer:

nataly862011 [7]3 years ago

7 0

Answer:

Length = 4 feet

Width = 4 feet

Step-by-step explanation:

The perimeter of a rectangle formula = 2L + 2W

Where L = Length

W = Width

The length of a rectangle is 8feet less than the width.

Hence,

L = 8 - W

The perimeter is 64 feet.

Hence,

64 = 2(8 - W) × 2W

64 =( 16 - 2W )2W

64 = -4W² + 32W

4W² - 32W + 64 = 0

Factorise

4W² - 16W - 16W + 64 = 0

4W (W - 4) - 16(W - 4) = 0

W - 4 = 0

W = 4

Width = 4

Solving for L

L = 8 - W

L = 8 - 4

L = 4

Therefore,

Length = 4 feet

Width = 4 feet

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