Question

The width and length of a rectangle (in feet)are consecutive odd integers. If the length is increased by 5 feet, the area of the resulting rectangle is 60 square feet. What is the area of the original rectangle?
A. 25 ft^2
B. 30 ft^2
C. 35 ft^2

Answer 1

Answer:

Option C is correct.

Step-by-step explanation:

Let x be the original width

then x+2 will be the length (consecutive odd integer)

if length is increased by 5 feet , length will be: (x+2)+5 = x+7

Area = 60 square ft.

Area = length * width

60 = (x+7) *x

60 = x^2 +7x

Rearranging

x^2 + 7x -60 = 0

Solving quadratic equation to find the value of x

using Quadratic formula

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

a=1, b =7, c=-60

$x=\frac{-7\pm\sqrt{(7)^2-4(1)(-60)}}{2(1)}\\x=\frac{-7\pm\sqrt{49+240}}{2}\\x=\frac{-7\pm\sqrt{289}}{2}\\x=\frac{-7\pm17}{2}\\x=5 \,\, and \,\, x = -12$

Since width can be positive so x=5

length of original rectangle = x+2 = 5+2 =7

Area of original rectangle = Length * Width

Area of original rectangle = 5 * 7

Area of original rectangle = 35 ft^2

So, Option C is correct.