Question

Can someone answer question 10-11-12 for me.

Book: Haese mathematics 8
Page: 434


This one:
The length of a rectangle is 4 cm more than its width , and the area of the rectangle is 96 cm ? Find the width of the rectangle .

Answer 1

Width of the rectangle is 12 cm.

Solution:

The length of a rectangle is 4 cm more than its width , and the area of the rectangle is 96 cm². Find the width of the rectangle.

Given data:

Let x be width of the rectangle.

Length of the rectangle = (x + 4) cm

Area of the rectangle = 96 cm²

length × breadth = 96

`(x+4)* x =96`

`x^2+4x=96`

Subtract 96 from both sides.

`x^2+4x-96=0`

Let us factor the polynomial.

`x^2+8x-12x-96=0`

Take x common in 1st two terms and -12 common in next two terms.

`x(x+8)-12(x+8)=0`

Now, take (x + 8) common in both terms.

`(x+8)(x-12)=0`

x + 8 = 0 and x - 12 = 0

x = -8 and x = 12

Dimension cannot be in negative terms, so ignore x = -8.

Width = 12 cm

Width of the rectangle is 12 cm.