Question

What is the length of the missing side of the triangle in simplest radical form? The figure is not drawn to scale.

Answer 1

`4 √(34) cm`

EXPLANATION

The missing side is the hypotenuse of the right triangle.

According to the Pythagoras Theorem, the length of the square of the hypotenuse is equal to the sum of the length of the squares of the two shorter legs.

Let the hypotenuse be x.

Then,

`{x}^(2) = {20}^(2) + {12}^(2)`

`{x}^(2) = 400 + 144`

`{x}^(2) = 544`

Take positive square root of both sides.

`x = √(544)`

`x = 4 √(34)`

Answer 2

4√34

Explanation:

the question asks for the value of the hypotenuse

Applying the Pythagorean equation

a²+b²=c² where a=12cm, b=20cm and c?

substituting values to equation

12²+20²=c²

144+400=c²

544=c²

√544=c

√16 × √34 =c

4×√34

4√34