Question

the perimeter of a right triangle is 30 cm. If it's hypotenuse is 13 cm, then what are the other two sides of the triangle

Answer 1

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Answer 2

Answer:

The other two sides of the triangle are 12 cm and 5 cm

Step-by-step explanation:

Let the other two sides of triangle be x and y

It's hypotenuse is 13 cm

Perimeter of triangle = Sum of all sides

                                  = x+ y+13

We are given that the perimeter of a right triangle is 30 cm

So, $x+ y+13 = 30$

$x+ y = 30-13$

$x+ y = 17$  --1

$Hypotenuse^2=Perpendicular^2+Base^2$

$13^2=x^2+y^2$

$169=x^2+y^2$  ---2

Substitute the value of x from 1 in 2

$169=(17-y)^2+y^2$

$169=289+y^2-34y+y^2$

$169=289+2y^2-34y$

$2y^2-34y+120=0$

$y^2-12y-5y+60=0$

$y(y-12)-5(y-12)=0$

$(y-5)(y-12)=0$

$y=5,12$

When y = 5

x=17-y = 17-5 =12

When y = 12

x=17-y = 17-12 =5

So, the other two sides of the triangle are 12 cm and 5 cm