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

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=(1)/(2)* \text{base}* \text{height}`

`\Rightarrow A=(1)/(2)* (x+3)* (2x-5)\\\\\Rightarrow 40=(x+3)* (2x-5)\\\Rightarrow 2x^2+x-55=0\\\\\Rightarrow x=(-1\pm √(1^2-4(2)(-55)))/(2(2))\\\\\Rightarrow x=(-1\pm 21)/(4)\\\\\Rightarrow x=-5.5,5`

Neglecting negative value

Therefore, the value of x is 5.