Question

A right triangle has sides 20 and 48. Use the Pythagorean Theorem to find the length of the hypotenuse

Answer 1

Answer: Let the length of the hypotenuse be x

Applying the Pythagorean theorem we have :

x²=20²+48²

⇒x²=2704

⇒x=52( ∀ x >= 0 )

Explanation:

Answer 2

Let assume the hypotenuse(longest side of right triangle) be x

By Pythagoras theorem

`\bf \large \longrightarrow \: {c}^(2) \: = \: {a}^(2) \: + \: {b}^(2)`

• c = x
• a = 20
• b = 48

Applying Pythagoras theorem

`\bf \large \implies \: {x}^(2) \: = \: {20}^(2) \: + \: {48}^(2)`

`\bf \large \implies \: {x}^(2) \: = \:400 \: + \: 2304`

`\bf \large \implies \: {x}^(2) \: = \:2704`

`\bf \large \implies \: √(x) \: = \: √(2704)`

`\bf \large \implies \: \: x \: = \: 52`

Hence , the length of hypotenuse is 52.