Question

The length of a rectangle is 9 centimeters less than its width. What are the dimensions of the rectangle if its area is 136 square​ centimeters?

Answer 1

Step-by-step explanation:

let the breadth be x

then length will be x -9

Area = length × breadth

136 = (x - 9) × x

136 = x² - 9x

0 = x² - 9x - 136

0 = x² + 8x - 17x -136

0 = x(x + 8) - 17 (x + 8)

0 = (x - 17) ( x + 8)

x = 17 or x = -8

since length cannot be negative

x = 17

length = 17 - 9 = 8cm

breadth = 17 cm

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Answer 2

Let width be x

Therefore, length is x - 9

Area of rectangle = lenght * breadth

136 = (x - 9)(x)

136 = x² - 9x

x² - 9x - 136 = 0

x² - 17x + 8x -136 = 0

(x² - 17x) + (8x - 136) = 0

x(x - 17) + 8(x - 17) = 0

(x + 8)(x - 17) = 0

Therefore, x = -8 which is not possible

Hence, x = 17 lenght is always positive

Width = 17cm

Lenght = 17 - 9 = 8cm

Hope it helps you!!!