Answer:
[tex]x^2+10x=144[/tex]
Step-by-step explanation:
Given : The length is 10 inches longer than its width.
Area of rectangle is 144 sq.inches
To Find : Define a variable for the width and set up an equation to find the dimensions of a rectangle
Solution:
Let the width be x
Since we are given that The length is 10 inches longer than its width.
So, Length of rectangle = x+10
Area of rectangle = [tex]Length \times Width[/tex]
= [tex]x \times (x+10)[/tex]
We are given that Area of rectangle is 144 sq.inches
So, [tex]x \times (x+10) =144[/tex]
[tex]x^2+10x=144[/tex]
[tex]x^2+18x-8x-144=0[/tex]
[tex]x(x+18)-8(x+18)=0[/tex]
[tex](x+18)(x-8)=0[/tex]
[tex]x=-18,8[/tex]
Since width cannot be negative
So, width of rectangle is 8 inches
Length of rectangle = x+10 = 8+10 = 18
Hence an equation to find the dimensions of a rectangle that has an area 144 square inches is [tex]x^2+10x=144[/tex]
