Question

The length of the hypotenuse of a right triangle is 1cm more than triple that of the shorter leg. The length of the longer leg is 1cm less than triple that of the shorter leg. Find of the lengths of the three sides of the triangle

Answer 1

The length of the shorter leg is 12 cm

The length of the longer leg is 35 cm

The length of the hypotenuse is 37 cm

Explanation:

Let

x ----> the length of the shorter leg

y ----> the length of the longer leg

z ----> the length of the hypotenuse

we know that

`z=3x+1` ----> equation A

`y=3x-1` ----> equation B

Remember that in a right triangle we can apply the Pythagorean Theorem

so

`z^2=x^2+y^2` ----> equation C

substitute equation A and equation B in equation C

`(3x+1)^2=x^2+(3x-1)^2`

solve for x

`9x^2+6x+1=x^2+9x^2-6x+1`

simplify

`6x=x^2-6x`

`x^2-12x=0`

`x(x-12)=0`

The solutions are x=0 cm, x=12 cm

therefore

The solution is x=12 cm

Find the value of y

`y=3(12)-1=35\ cm`

Find the value of z

`z=3(12)+1=37\ cm`

therefore

The length of the shorter leg is 12 cm

The length of the longer leg is 35 cm

The length of the hypotenuse is 37 cm