Answer:
L= 18 in
W= 8 in
Step-by-step explanation:
Step one:
The length of a rectangle is 10 inches longer than its width
let the width be x
so the lenght is x+10
the area of the rectangle is 144 square inches
Step two:
[tex]Area= L*W\\\\144=x(x+10)\\\\144=x^2+10x\\\\x^2+10x-144=0[/tex]
the factors for the quadratic expression is
18 and -8
[tex]x^2+18x-8x-144=0\\\\x(x+18)-8(x+18)=0\\\\x-8=0\\\\x=8\\\\x+18=0\\\\x=-18[/tex]
the width is 8 in
the length is 8+10= 18 in
From the equation, the length is 18 inches and the width is 8 inches.
Let width = w
Since the length of a rectangle is 10 inches longer than its width, the length will be w+10.
Area = 144 inches²
Area = Length × Width
w(w + 10) = 144
w² + 10w = 144
w² + 18w - 8w - 144 = 0
w(w + 18) - 8(w + 18) = 0
(w - 8) = 0
w = 0 + 8 = 8
Length = w + 10 = 8 + 10 = 18
Learn more about equations on:
https://brainly.com/question/2972832
