Question

The area of a triangle is 10 cm2. Its base is 3 cm less than twice its height. What is the height of the triangle?

Answer 1

The height of the triangle = 4cm

Explanation:

Given, area of the triangle = 10
`cm^(2)`

Let the height of the triangle be h cm

Given, the base b is 3 cm less than twice its height.

b = 2h - 3 ... (1)

By formula, area of the triangle =
`(1)/(2)` bh .. (2)

substitute (1)in (2), we get

Area =
`(1)/(2)` (2h-3) h

10 =
`(1)/(2)` (2h-3) h

20 =
`2h^(2) - 3h`

`2h^(2) - 3h` - 20 = 0

solving the equation, we get x = 4, -2.5

The height of the triangle = 4cm