The length of a rectangle is 4 feet shorter than its width. the area of the rectangle is 42 square feet. find the length and width. round your answer to the nearest tenth of a foot
Mathematics · High School · Thu Feb 04 2021
Answered on
Let the width be x
Then, Length would be x - 4
Area of rectangle = 42 sq. Feet
Formula Used : Area of rectangle = l × w
42 = x × ( x-4)
42 = x² - 4x
Transposing 42 to other side, we get
x² -4x -42 =0
Using quadratic formula
x = -b ±√b²-4ac/2a
x = -(-4)±√-4² - 4(1)(-42)/2×1
x = 4 ±√16 + 168/2
x = 4±√184/2
x = 2±√46
x = 2±6.8
Now, taking positive sign, we get
x = 2 + 6.8
x = 8.8
Taking negative sign, we get
x = 2 - 6.8
x = -4.8
So the width of rectangle is 8.8
Then, Length of rectangle = w -4
= 8.8 - 4
= 4.8
Rounding these to nearest foot we get Length and width of rectangle as 5 foot and 9 foot respectively.