Question

a rectangle has length 3 cm greater than it’s width. If it has an area of 28cm 2, find the dimensions of the rectangle

Answer 1

The length of the rectangle is 7 centimeter and the width of the rectangle is 4 centimeter

A rectangle has length 3 cm greater than it’s width

Consider the width of the rectangle = x

The length of the the rectangle = x + 3

The area of the rectangle = 28 square centimeter

The area of the rectangle = The length of the the rectangle × The width of the rectangle

Substitute the values in the equation

x(x+3) = 28

Apply the distributive property

$x^2$  + 3x = 28

$x^2$ + 3x -28 = 0

Split the middle term and solve the equation

$x^2$ -4x + 7x -28 = 0

Take common term outside

x(x-4) + 7(x-4) =0

Take common term outside

(x+7) (x-4) = 0

x = -7, 4

The length cannot be negative value

x = 4 centimeter

Then the length of the rectangle = x + 3

= 4 +3

= 7 centimeter

Hence, the length of the rectangle is 7 centimeter and the width of the rectangle is 4 centimeter

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