Question

The perpendicular height of triangle is (2x-5)cm and the base measures (x+3)cm. The area of this triangle is 20cm^2.
Find the length of the base.

Answer 1

Answer:

length of the base = 8 cm

Step-by-step explanation:

Given:

height of the triangle (h) = (2x-5)cm

base of the triangle (b) = (X+3) cm

area of the traingle (a) = 20cm²

from area of traingle formula,

a= 1/2 * b * h

20 = 1/2 (2x-5) (X+3)

(2x-5) (X+3) = 40

2x²-5x+6x -15-40 = 0

2x²+x-55 = 0

2x²+11x-10x -55=0

x(2x+11) -5(2X+11)=0

(x-5)(2x+11) = 0

X= 5, X= -11/2

but if we use X=-11/2, height will be -16 cm, which is not possible as height can only be positive.

so, X= 5

length of the base = 5+3 = 8 cm