Question

The area of a triangle piece of stained glass is 50 centimeters if the height of the triangle is four times the base, how long are the height and base of the piece of stained glass

Answer 1

base=5 cm, height = 20cm

EXPLANATION

The area of a triangle is

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

From the question, A=50 and h=4b

We substitute into the formula to get;

`(1)/(2) b * 4b =5 0`

This implies that,

`2 {b}^(2) = 50`

`{b}^(2) = 25`

Take positive square root to get;

`b = √(25)`

`b = 5`

The base is 5 cm and the height is 20 cm.

Answer 2

Base = 5 cm

Height = 20 cm

Explanation:

Points to remember

Area of triangle = bh/2

Where b - base of triangle

h - Height of triangle

To find the Height and Base of given triangle

It is given that,area of a triangle piece of stained glass is 50 centimeters

the height of the triangle is four times the base

h = 4b

Area = bh/2

50 = (b * 4b)/2

100 = 4b²

b² = 100/4 = 25

b =√25 = ±5

b = 5 then h = 4b = 4 * 5 = 20

Base = 5 cm and Height = 20 cm