Question

The height of a triangle is 8 m more than the length of the base. The area of the triangle is 21 m^2. Find the height of the triangle​

Answer 1

height = 12 cm

Explanation:

Area of a triangle is given by

`A = (1)/(2) bh`

where

b is the base

h is the height

From the question

Area = 21 m²

The statement

The height of a triangle is 8 m more than the length of the base is written as

h = 8 + b

Make b the subject

That's

b = h - 8

Substitute the expression into the above formula and solve for the height

That's

`21 = (1)/(2) (h - 8)h`

Multiply through by 2

h² - 8h = 48

h² - 8h - 48 = 0

(h + 4)(h - 12) = 0

h + 4 = 0 h - 12 = 0

h = - 4 h = 12

Since the height cannot be a negative number we have the final answer as

height = 12 cm

Hope this helps you