Answer with work please

Mathematics

1 answer:

Delicious77 [7]3 years ago

4 0

Okayy what that is uh huh ?

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

Eva8 [605]

Answer: 1. x= 20 units, 2. x= $5\sqrt{3}$ units 3. x= $4\sqrt{2}$ units.

Step-by-step explanation:

In a right triangle,

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

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

$\Rightarrow\ x^2 =12^2+16^2\\\\ \Rightarrow\ x^2=144+256\\\\ \Rightarrow\ x^2=400\\\\ \Rightarrow\ x=\sqrt{400}=20$

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

$\Rightarrow\ 14^2=x^2+11^2\\\\\Rightarrow\ 196=x^2+121\\\\\Rightarrow\ x^2=196-121\\\\\Rightarrow\ x^2 = 75\\\\\Rightarrow\ x=\sqrt{75}=\sqrt{25\times3}=5\sqrt{3}$

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

$\Rightarrow\ 9^2=x^2+7^2\\\\\Rightarrow\ 81= x^2+49\\\\\Rightarrow\ x^2=81-49\\\\\Rightarrow\ x^2=32\\\\\Rightarrow\ x=\sqrt{32}=\sqrt{16\times2}\\\\\Rightarrow\ x=4\sqrt{2}$