Question

Find the unknown side length. Write your answer in simplest radical form.

Answer 1

Answer: 1. x= 20 units, 2. x=
`5√(3)` units 3. x=
`4√(2)` units.

Explanation:

In a right triangle,

`Hypotenuse^2= Perpendicular^2+Base^2` (Pythagoras theorem)

1. Hypotenuse = x , Base = 16, Perpendicular = 12

`\Rightarrow\ x^2 =12^2+16^2\\\\ \Rightarrow\ x^2=144+256\\\\ \Rightarrow\ x^2=400\\\\ \Rightarrow\ x=√(400)=20`

2. Hypotenuse = 14 , Base = 11, Perpendicular = x

`\Rightarrow\ 14^2=x^2+11^2\\\\\Rightarrow\ 196=x^2+121\\\\\Rightarrow\ x^2=196-121\\\\\Rightarrow\ x^2 = 75\\\\\Rightarrow\ x=√(75)=√(25*3)=5√(3)`

3. Hypotenuse = 9 , Base = x, Perpendicular =7

`\Rightarrow\ 9^2=x^2+7^2\\\\\Rightarrow\ 81= x^2+49\\\\\Rightarrow\ x^2=81-49\\\\\Rightarrow\ x^2=32\\\\\Rightarrow\ x=√(32)=√(16*2)\\\\\Rightarrow\ x=4√(2)`