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

Answer:

The height of the triangle = 4cm

Step-by-step 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 = $\frac{1}{2}$ bh .. (2)

substitute (1)in (2), we get

Area = $\frac{1}{2}$ (2h-3) h

10 = $\frac{1}{2}$ (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