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# what is the longest side of the rectangle?

A rectangle measures x+10 cm and x-10 cm, squares of side 3 cm are taken from each corner. The resulting shape has an area 264cm2. Find the length of the longest side of the rectangle

### 3 Answers

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• Total area = 264cm² + 2*(3cm x 3 cm) = 283 cm²

283 cm² = (x+10 cm) (x-10 cm) = x² -100

x = √383

x + 10 = 10 + √383 cm = 29.57 cm

•   A rectangle measures (x + 10) cm by (x - 10) cm.

Squares of side 3 cm are taken from each corner.

The resulting shape has an area of 264 cm^2.

(x + 4)(x - 16) = 264

x^2 - 12x - 328 = 0

x ≈ 25.079 cm

The length of the longest side of the rectangle is 25.079 cm.

• A(rectangle) = ( x + 10)(x - 10) = x^2 - 100

The four corners are 4 x 3 x 3 = 36cm^2

Hence

x^2  - 100 - 36 = 264

x^2 = 136 + 264

x^2 = 400

x = +/-20

x = 20

Hence longest side is 20 + 10 = 30 cm

& shortest side is 20 - 10 = 10 cm

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