Question

The base of a right triangle is 13 less than 2 times the height. The area of the triangle is 12 square cm. What is the height of the triangle in cm? *

Answer 1

The height of the triangle is 8 cm

Explanation:

First we need to write down the question in a mathematical format and then solve.

let b be the base of the triangle and h be the height of the triangle

"The base of a right triangle is 13 less than 2 times the height" can be written as

b = 2h - 13 -----------------------------------------------------(1)

"The area of the triangle is 12 square cm" can be written as;

area of the triangle = 12 cm²

but area of a triangle =
`(1)/(2)` ×b × h

This implies that

`(1)/(2)` ×b × h = 12 cm²

bh = 24 cm² --------------------------------------------------(2)

substitute equation (1) in equation (2)

(2h - 13)h = 24

2h² - 13h = 24

2h² - 13h - 24 = 0 ----------------------------------------------(3)

The above is now a quadratic equation, so we will solve by completing the square method.

Find two numbers such that its product will give -48 and its sum will give -13

The two numbers are -16 and 3

Replace -13h by (-16h + 3h) in equation (3)

2h² - 13h - 24 = 0

2h² - 16h + 3h - 24 = 0

2h(h - 8) + 3(h-8) = 0

(h-8)(2h+3) = 0

either h-8 = 0

h = 8

OR

2h + 3 = 0

2h = -3

h =-3/8

There is no such thing as negative length, therefore h= 8 is the answer

The height of the triangle is 8 cm