Question

In a right triangle, 1/5 of the length of the longer leg is equal to 7/12 of the length of the shorter leg. What is the ratio of the length of the hypotenuse to the length of the longer leg?

Answer 1

37/35

Answer 2

and can u explain how u got that?

Answer 3

step by step

Answer 4

(1/5)L = (7/12)S
Therefore:
L = (5)(7/12)S = (35/12)S

S = S
L = (35/12)S

Pythagorean Theorem:
a^2 + b^2 = c^2

\[c=\sqrt(a ^{2}+b ^{2})\]

Answer 5

\[Hypotenuse = \sqrt{S^{2}+L ^{2}}\]

Answer 6

\[H = \sqrt{(S)^{2}+((35/12)S)^{2}} = {37 \over 12}S\]

Answer 7

We want the ratio of Hypotenuse:LongerSide

Answer 8

H:L = \[H:L = {37 \over 12}S:{35 \over 12}S\]

Answer 9

The S's and 12's cancel each other out.

Answer 10

Leaving us with:

37:35

or

37/35

Answer 11

Make sense?

Answer 12

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