Question

Base and height of triangle are (x+3)cm and (2x-5)cm respectively. If the area is 20cm², find x

Answer 1

Solution :-

Given : Base and height of triangle are (x+3) cm and (2x-5) cm respectively.

Area = 20 cm²

Formula to find area of triangle :

= ½ × Base × Height Sq. units

According to the question,

=> ½ (x + 3) (2x - 5) = 20

=> 2x² - 5x + 6x - 15 = 20 × 2

=> 2x² + x - 15 = 40

=> 2x² + x - 15 - 40 = 0

=> 2x² - 10x + 11x - 55 = 0

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

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

=> x = - 11/2 or x = 5

∴ x = 5 (Length is always positive)

Hence,

The value of x = 5 cm

Answer 2

Answer

Area of triangle = 1/2 × base × height

=> 20 = 1/2 × (x+3) × (2x-5)

=> 40 = 2x^2 - 5x + 6x - 15

=> 2x^2 + x - 55 = 0

Roots of this equation:-

2x^2 + x - 55 = 0

=> -11/2, 5

Length needs to be positive, thus:

x = 5 cm