Question

The area of a triangle is 2x^2 - 11x + 15 square meters. The length of the base of the triangle is 2x-5

meters. What is the height of the triangle?

Answer 1

2x-6

Explanation:

height : 2(2x^2-11x+15)/(2x-5)

(4x^2-22x+30)/(2x-5)

Δ/4 = 121 - 120 = 1

x1 = (11+1)/4 = 3

x2 = (11-1)/ 4 = 5/2

4(x-5/2)(x-3)

(4x-10)(x-3)/(2x-5)

2(2x-5)(x-3)/(2x-5)

2x-6

Proof

(2x-6)(2x-5)/2

2(x-3)(2x-5)/2

2x^2-5x-6x+15

2x^2-11x + 15

Answer 2

of triangle =12base×height

Area of triangle =2x2−11x+15

base =2x−5

Plugging in the given;

2x2−11x+15=12(2x−5)×height

2x2−11x+15=2x−52×height

2x2−11x+151=2x−52×height

2(2x2−11x+15)=(2x−5)×height

4x2−22x+30=(2x−5)×height

4x2−22x+302x−5=height

Resolving the quadratic equation;

(4x2−22x+30)

Simplifying;

4x