A landscaper wants to create a 12-foot-long diagonal path through a rectangular garden. The width of the garden is x feet and the length of the garden is 4 more than the width. He uses the Pythagorean theorem to write an equation to determine the width of the garden. (x) 2 + (x + 4) 2 = (12) 2 x2 + x2 + 8x + 16 = 144 2x2 + 8x - 128 = 0 What are the approximate dimensions of the garden? 6.2 ft by 2.2 ft 6.2 ft by 10.2 ft 10.2 ft by 2.2 ft

Question

Julianne West

Mathematics

13 December, 12:07

A landscaper wants to create a 12-foot-long diagonal path through a rectangular garden. The width of the garden is x feet and the length of the garden is 4 more than the width. He uses the Pythagorean theorem to write an equation to determine the width of the garden. (x) 2 + (x + 4) 2 = (12) 2 x2 + x2 + 8x + 16 = 144 2x2 + 8x - 128 = 0 What are the approximate dimensions of the garden? 6.2 ft by 2.2 ft 6.2 ft by 10.2 ft 10.2 ft by 2.2 ft

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Ruiz · Answer 1

If we let x be the width of the garden, then x+4 will be the length. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs.

12² = (x) ² + (x + 4) ²

Simplifying,

144 = x² + x² + 8x + 16

Further simplification,

144 = 2x² + 8x + 16

x² + 4x - 128 = 0

The value of x from the equation is 6.2 ft. The length is then equal to 10.2 ft.

The answer to this item is the second choice.