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

the correct answer would be 35ft^2

Answer 2

Option C is correct.

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=(-b\pm√(b^2-4ac))/(2a)`

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

`x=(-7\pm√((7)^2-4(1)(-60)))/(2(1))\\x=(-7\pm√(49+240))/(2)\\x=(-7\pm√(289))/(2)\\x=(-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.