Question

A sail is in the form of a right triangle that is three times as high it is wide. The sail is made from 24 square meters of materials. What is its height

Answer 1

A sail is in the form of a right triangle that is three times as high it is wide. The sail is made from 24 square meters of materials. What is its height?

The height is 12

Answer 2

Make an equation system based on the problem
First equation
An equation for "a right triangle that is three times as high it is wide" could be written as:
∴ h = 3b (b stands for the wide/base, h stands for the height)
Second equation
An equation for "The sail is made from 24 square meters of materials" could be written as:
∴ area = 24

`(1)/(2)bh=24`

Solve the system of equation by substitution method.
Substitute h with 3b in the second equation, and we'll find the value of b

`(1)/(2)bh=24`

`(1)/(2)b(3b)=24`
simplify

`(3 b^(2) )/(2) =24`

Solve for b
3b² = 24 × 2
3b² = 48
b² = 48/3
b² = 16
b = √16
b = 4
The value of b is 4, therefore the base of the triangle is 4 meters wide.

Using first equation, find the value of h
h = 3b
h = 3(4)
h = 12
The height of the triangle is 12 meters