Question

The length of a rectangle is 4 inches greater than the width. If each dimension is increased by 3 inches, the new area will be 99. square inches larger. Find the length of the original rectangle. es ) W A) 11 inches B) 13 inches 15 inches D) 17 inches ?

Answer 1

The length of a rectangle is 4 inches greater than the width

Let the width = x

as length of a rectangle is 4 inches greater than the width

Length of rectangle = 4 + Width

Length =4 + x

Thus, the original measurements are :

Length = x + 4 and width = x

Area of the original rectangle = x(X + 4)

If each dimension is increased by 3 inches, the new area will be 99. square inches larger.

New dimension = 3 + Original dimenstion

New length = x + 4 + 3 = x + 7

New width =x + 3

Area of new rectangle = (x+3)(x+7)

as the new area will be 99. square inches larger.

i.e. New area = 99 + Original area

New area = 99 + x(x+4)

(x+3)(x+7)=99+x(x+4)

Simplify the expression for x :

$\begin{gathered} (x+3)(x+7)=99+x(x+4)_{} \\ x^2+10x+21=99+x^2+4x \\ 10x-4x=99-21 \\ 6x=78 \\ x=\frac{78}{6} \\ x=13 \end{gathered}$

x = 13

so, width = 13cm and for length :4 + x

Length = 13 + 4

Length = 17cm

Length = 17cm and width = 13cm

Answer : Dimension of original rectangle :Length = 17cm and width 13cm