Question

What is the length of leg y of the right triangle?

84
85
O1
09
O 13
O 26

Answer 1

Answer : 13

Step-by-step explanation:

(Using Pythagoras Theorem)

c^2 - a^2 = b^2
85^2 - 84^2 = b^2
7225 - 7056 = b^2
169 = b^2
√169 = b
b= 13

I HOPE THIS HELPED:)

Answer 2

`\boxed{\sf Length \ of \ leg \ y = 13}`

Step-by-step explanation:

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

`\therefore \\ \sf \implies {84}^(2) + {y}^(2) = {85}^(2) \\ \\ \sf {84}^(2) = 7056 : \\ \sf \implies 7056 + {y}^(2) = {85}^(2) \\ \\ \sf {85}^(2) = 7225 : \\ \sf \implies 7056 + {y}^(2) = 7225 \\ \\ \sf Substract \: 7056 \: from \: both \: sides : \\ \sf \implies (7056 - 7056) + {y}^(2) = 7225 - 7056 \\ \\ \sf 7056 - 7056 = 0 : \\ \sf \implies {y}^(2) = 7225 - 7056 \\ \\ \sf 7225 - 7056 = 169 : \\ \sf \implies {y}^(2) = 169 \\ \\ \sf 169 = {13}^(2) : \\ \sf \implies {y}^(2) = {13}^(2) \\ \\ \sf \implies y = \sqrt{ {13}^(2) } \\ \\ \sf \implies y = {13}^{ \cancel{2} * \frac{1}{ \cancel{2}} } \\ \\ \sf \implies y = 13`

So,

Length of leg y of the right triangle = 13