Question

The hypotenuse of right angle is 6 more than the twice of the shortest side. if the third side is 2m less than the hypotenuse then find the shortest side of the triangle...plzzzz it's very urgent

Answer 1

Let x = shortest side
then
2x+6 = hypotenuse
2x+6-2 = 2x+4 = long side
.
x^2 + (2x+4)^2 = (2x+6)^2
x^2 + (2x+4)(2x+4) = (2x+6)(2x+6)
x^2 + 4x^2+16x+16 = 4x^2+24x+36
5x^2+16x+16 = 4x^2+24x+36
x^2+16x+16 = 24x+36
x^2-8x+16 = 36
x^2-8x-20 = 0
(x-10)(x+2) = 0
x {-2, 10}
throw out the negative solution leaving:
x = 10m (short side)
.
hypotenuse:
2x+6 = 2(10)+6 = 20+6 = 26m
.
long side:
2x+4 = 2(10)+4 = 20+4 = 24m

Answer 2

HEYA!!!!!

Let the shortest side = x

Hypotenuse side = 2x + 6

Third side = 2x + 6-2

= 2x + 4

From pythagorus therom,

${AC}^{2} = {AB}^{2} + {BC}^{2}$

( 2x +6 ) ^2 = x^2 +( 2x +4)^2

(2x)^2 + 2 (2x) (2) + 6^2 = x^2 + ( 2x)^2 + 2 (2x ) (4) +4^2

4x^2 + 24x + 36 = x^2 + 4x^2 + 16x + 16

0 = x^2 + 1 6x -24 x 16-36

x^2 - 8x -20 = 0

x ^2 - 10 x + 2x - 20 = 0

x ( x-10) + 2 ( x -10 ) =0

(x-10) (x+2) = 0

x - 10 =0 x +2 = 0

x = 10 ,, x = -2

We know the sides are always positive.

Therefore, the shortest side = 10

hypotenuse side = 2(10) +6 = 20+6 = 26

Third side = 2 (10) +4 = 20 + 4 = 24....

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HOPE THIS HELPS U.