The area of a rectanle is 180 square centimeters. the height is six more than 4 times the base. what is the perimeter
Mathematics · High School · Wed Jan 13 2021
Answered on
Given :
Area of rectangle = 180 sq. Cm
Let the base be x
Then, height(width) be 4x + 6
So, Area of rectangle = Length × width
180 = x × (4x + 6)
180 = 4x² + 6x
4x² + 6x - 180 = 0
Or, 2x² + 3x - 90 = 0
By middle-term split method
2x² + 15x - 12x - 90 =0
x(2x + 15) - 6(2x + 15) =0
(x -6)(2x + 15) = 0
Length cannot be in negative
So, x = 6
So, base = 6
Width = 4(6) +6
= 24 +6
= 30
So, Perimeter = 2(l+ w)
= 2(6 + 30)
= 2(36)
= 72
Thus, Perimeter of rectangle is 72 cm