Question

The length and width of a rectangle can be expressed as x+3 and x-8 . If the area of the rectangle is 60 square inches , what is the value of x?

Answer 1

The length and width of a rectangle can be expressed as x+3 and x-8 . If the area of the rectangle is 60 square inches , what is the value of x? ​

Remember that

the area of rectangle is

A=L*W

we have

L=x+3

W=x-8

substitute

A=(x+3)(x-8)

A=60 in2

so

60=(x+3)(x-8)

solve for x

x^2-8x+3x-24=60

x^2-5x-24-60=0

x^2-5x-84=0

solve the quadratic equation using the formula

we have

a=1

b=-5

c=-84

substitute

`x=\frac{-(-5)\pm\sqrt[\square]{-5^2-4(1)(-84)}}{2(1)}`
`\begin{gathered} x=\frac{5\pm\sqrt[\square]{361}}{2} \\ \\ x=(5\pm19)/(2) \end{gathered}`

the solutions are

x=12 and x=-7 (is not a solution)

therefore

the value of x is 12

verify

For x=12

L=12+3=15

W=12-8=4

Area=15*4=60 in2 -----> is ok