Question

The hypotenuse of a right triangle is 3 less than twice the length of

the shorter leg. Find the length of the hypotenuse if the longer leg

is 12 cm​

Answer 1

Let x be the length of the shorter leg. The hypotenuse is therefore 2x-3 and the other leg is x+3 long.

Using Pythagoras: (2x-3)²=x²+(x+3)².

So 4x²-12x+9=x²+x²+6x+9=2x²+6x+9; 2x²=18x, 2x=18 and x=9.

The shorter leg is 9 units long.

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Answer 2

Step-by-step explanation:

hypotenuse = H

hypotenuse = ($\sqrt[]{S^{2} + L^{2} }$)

shorter leg = S

longer let = L

Then,

hypotenuse = 3-$S^{2}$

shorter leg = S

longer let = 12 cm

according to Pythagorean theorem :-

$S^{2}$ + $L^{2}$ = $H^{2}$

So:

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