Question

Find the exact value of x.

Answer 1

1) 13 **Explained below **

2) 4 **Explained below **

3) 6

4) 8

5) 15

6) 2.64575 **Explained below **

Explanation:

All 6 problems can be solved using the Pythagorean theorem using the following two rules

If x is the hypotenuse and a, b are the shorter sides then

`x = √(a^2 + b^2)`

If x is one of the shorter sides and a (or b) is the other shorter side and c is the hypotenuse then


`x = \sqrt{c^2 - a^2\\` if a is the other shorter side

`x = \sqrt{c^2 - b^2\\` if b is the other shorter side

I will just demonstrate for #1 , #2 and #6. You can figure out the reasoning behind the rest.

#1. x is the hypotenuse, 5 and 12 are legs(shorter sides)

`x = √(5^2 + 12^2)\\\\x = √(25 + 144)\\\\x = √(169)\\\\x = 13\\\\`

# 2. x is one of the shorter sides (leg)

5 is the hypotenuse and 3 is the other shorter side

`x = \sqrt{5^(2) - 3^(2)}\\\\x = \sqrt{5^(2) - 3^(2)}\\\\x = √(25 - 9)\\\\x = √(16)\\\\x = 4`

#6 hypotenuse is 4, short side = 3

`x = \sqrt{4^(2) - 3^(2)}\\\\x = \sqrt{4^(2) - 3^(2)}\\\\x = √(16 - 9)\\\\x = √(7)\\\\x = 2.64575\\\\`