when the lengths of two opposite sides of a square garden were increased by x meters each and the lengths of the other two sides were decreased by x meters each, the area of the new garden was 64 square meters. what was the area of the original square garden?

Respuesta :

the area of the original square garden is 80 square meters.

Let the side of the original square be a. We are given that the area of the new garden was (a - x)(a + x) = a² - x² = 64.

We want to find the area of the original square, so the value of a².

(1) The area of the new garden was 80 percent of the area of the original square garden --> 64 = 0.8a² --> a² = 80. Sufficient.

(2) x = 4 --> a² - 4² = 64 --> a² = 80. Sufficient.

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