Question

A rectangle has a length 10 more than its width. If the width is increased by 8 and the length by 4, the resulting rectangle has an area of 135 square units.
Part A Write an equation to model the above scenario. Use the model to find the length of the original rectangle?
Part B What is the perimeter of the expanded rectangle?

Answer 1

The equation to model the above scenario is $x^{2}$ +22x - 23 = 0

The perimeter of the expanded rectangle is 48 units

What is a rectangle?

A rectangle is a quadrilateral with its 4 angles 90°

Analysis:

First rectangle:

length = 10 + x

width = x

Second rectangle:

length = x + 14

width = x + 8

Area of expanded rectangle = 135 square unit

(x+8)(x+14) = 135

$x^{2}$ + 8x + 14x + 112 = 135

$x^{2}$ + 8x + 14x -23 = 0

$x^{2}$ + 22x -23 = 0

$x^{2}$ + 23x - x - 23 = 0

(x-1)(x+23) = 0

Therefore x = 1

Expanded length = 1+14 = 15

Expanded width = 1+8 = 9

Perimeter = 2(9+15) = 48 units

Learn more about Rectangles: brainly.com/question/25292087

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