Question

2. The width of a rectangle is 5 units less than the length. If the area is 150 square units, then find the dimensions of the rectangle.

Answer 1

Answer:

• The length = x = 15 units

• The width = x-5 = 10 units

Step-by-step explanation:

Let 'x' be the length of a rectangle

As the width of a rectangle is 5 units less than the length.

so

width of rectangle will be = w = x - 5 units

Area = 150 square units

Using the formula

Area = length × width

$150=\left(x\right)\left(x-5\right)$

$150=x^2-5x$

$x^2-5x=150$

Subtract 50 from both sides

$x^2-5x-150=150-150$

$x^2-5x-150=0$

$\left(x+10\right)\left(x-15\right)=0$

if

$ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)$

$x+10=0\quad \mathrm{or}\quad \:x-15=0$

$x=-10,\:x=15$

As length can not be negative. so

x = 15 units

Hence,

The length = x = 15 units

The width = x-5 = 15-5 = 10 units