Question

Find the unknown side length, x. write your answer in simplest radical form.

a. 14
b. 18
c. 2 square root 119
d. 14 square root 17

Answer 1

x = sqrt(24^2 - 10^2) = sqrt(576 - 100) = sqrt(476) = 2 sqrt(119)

Answer 2

Unknown side length is
`2√(119)`

C is correct.

Explanation:

We are given a right angle triangle whose two sides are 24 and 10.

As shown in figure 24 is longest side. It would be hypotenuse of triangle. 10 would be length of one leg and x would be length of another leg.

It is right angle triangle. Using pythagoreous theorem find out another leg (x)

Pythagoreous theorem:

`a^2+b^2=c^2`

where, a=x, b=10 and c=24

`x^2+10^2=24^2`

`x^2=576-100=476`

`x=√(476)`

`x=2√(119)`

Thus, Unknown side length is
`2√(119)`