Question

The length of a side and the corresponding height of a triangle are (x+3) cm and (2x-5) cm respectively. Given that thr area of the triangle is 20 cm^2, find the value of x.

Answer 1

Answer: 5

Step-by-step explanation:

Given

The length of a side is $x+3\ cm$

The height of a triangle is $2x-5\ cm$

Area of triangle is $20\ cm^2$

Area of triangle is given by

$\Rightarrow A=\dfrac{1}{2}\times \text{base}\times \text{height}$

$\Rightarrow A=\dfrac{1}{2}\times (x+3)\times (2x-5)\\\\\Rightarrow 40=(x+3)\times (2x-5)\\\Rightarrow 2x^2+x-55=0\\\\\Rightarrow x=\dfrac{-1\pm \sqrt{1^2-4(2)(-55)}}{2(2)}\\\\\Rightarrow x=\dfrac{-1\pm 21}{4}\\\\\Rightarrow x=-5.5,5$

Neglecting negative value

Therefore, the value of x is 5.