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
[tex](x+4)\times x =96[/tex]
[tex]x^2+4x=96[/tex]
Subtract 96 from both sides.
[tex]x^2+4x-96=0[/tex]
Let us factor the polynomial.
[tex]x^2+8x-12x-96=0[/tex]
Take x common in 1st two terms and -12 common in next two terms.
[tex]x(x+8)-12(x+8)=0[/tex]
Now, take (x + 8) common in both terms.
[tex](x+8)(x-12)=0[/tex]
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.
