Question

A square is transformed into a rectangle by increasing the length by 8m and the width by 5m. If the area of the resulting rectangle is 108m^2, algebraically determine the length of each side of the original square.

Answer 1

The length of each side of the original square is 4 m

How to calculate the area of a square?

A square each side x is transformed into a rectangle by increasing the length by 8 m. Thus, new length = x + 8

The new width increases by 5 m will be;

New width = x + 5

If the area of the resulting rectangle is 108 m², then we have;

(x + 5)(x + 8) = 108

x² + 13x + 40 = 108

x² + 13x - 68 = 0

x² + 17x - 4x - 68 = 0

x(x + 17) - 4(x + 17) = 0

(x + 17)(x - 4) = 0

x = 4 or -17

ignore negative

So side of square = 4 m

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