Question

in a right angle triangle length of the hypotenuse is 12 cm more its shortest side. the length of other side is 6 cm less than the hypotenuse ,then find the sides of right angle triangle​

Answer 1

Step-by-step explanation:

the sides are 6 , 12 and 18 .

Answer 2

The sides of right angle triangle​ 18 cm, 24 cm and 30 cm.

Step-by-step explanation:

Length of the shortest side = x

Length of the hypotenuse = h = 12 + x

Length of the third side = (h - 6) = 12+x -6 = 6+x

Applying Pythagoras theorem :

$(\text{Shortest side})^2+(side)^2=(Hypotenuse)^2$

$x^2+(6+x)^2=(12+x)^2$

$x^2+36+12x+x^2=144+x^2+24x$

$x^2-12x-108=0$

$x^2+6x-18x-108=0$

$x(x+6)-18(x+6)=0$

(x+6)(x-18)=0

x = -6 (reject)

x = 18 (accept)

The sides of right angle triangle​:

Length of the shortest side = x =18 cm

Length of the hypotenuse = h = 12 + x = (12 + 18)cm = 30 cm

Length of the third side = (h - 6) = 12+x -6 = 6+x = (6 + 18)cm = 24 cm

The sides of right angle triangle​ 18 cm, 24 cm and 30 cm.

Learn more about ; Pythagoras theorem and quadratic equation

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