The length of a rectangle is seven units more than it's width if the width is doubled and the length is increased by two the area is increased by 42 square Units find the dimensiones of the original rectangle

length = 10 units; width = 3 units

Step-by-step explanation:

Let the width = w

Then the length is w + 7

Original area: w (w + 7)

Double the width: 2w

Increase the length by 2: w + 9

Area of new rectangle: 2w (w + 9)

Area of new rectangle = w (w + 7) + 42

2w (w + 9) = w (w + 7) + 42

2w^2 + 18w = w^2 + 7w + 42

w^2 + 11w - 42 = 0

(w + 14) (w - 3) = 0

w + 14 = 0 or w - 3 = 0

w = - 14 or w = 3

A width cannot be negative, so we discard w = - 14.

The original width is 3 units.

The length is 7 more than the width, so the length is 10 units.

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