Question

The side lengths of a right triangle are 18 cm, 24 cm, and 30 cm. You are asked to find the area of the triangle by using A = 1/2bh.

1. How do you decide which side lengths to use?
2. Find the area of the right triangle.

Answer 1

Part 1) The lengths to use in the formula are 18 cm and 24 cm

Part 2) The area of the right triangle is
`216\ cm^2`

Explanation:

Part 1) How do you decide which side lengths to use?

we know that

The area of any triangle is given by the formula

`A=(1)/(2)(b)(h)`

If the triangle is a right triangle

then

The legs are the perpendicular sides and the hypotenuse is the greater side

so

In this problem

The hypotenuse is 30 cm

The legs are 18 cm and 24 cm

so

The lengths to use in the formula are the perpendicular legs

therefore

The lengths to use in the formula are 18 cm and 24 cm

Part 2) Find the area of the right triangle

`A=(1)/(2)(b)(h)`

Let

`b=18\ cm\\h=24\ cm`

substitute in the formula

`A=(1)/(2)(18)(24)=216\ cm^2`