Question

A circle with radius r is inscribed into a right triangle. Find the perimeter of the triangle if the length of the hypotenuse is 24 cm and r=4 cm;

Answer 1

Answer: 56

Explanation:

4=(a+b-24)/2

32=a+b

32+24=56

Answer 2

The perimeter of the triangle is 56 cm.

Explanation:

Given:

The length of the hypotenuse is 24 cm

Radius of the circle r=4 cm

To Find:

The perimeter of the triangle=?

Solution:

Let us see the below diagram representing situation.

Here, first we have drawn the radius of circle perpendicular to the sides of triangle,

We have Taken PB = 4 because, it is a side of square formed there, and we take OC as x.

Then, QC also becomes x as they are tangents from single point, so they are equal.

Now, AQ becomes 24 – x as AC is 24 according to given information.

So, perimeter = AB + BC + CA

Perimeter = (24 – x + 4) + (4 + x) + (24 – x + x)

Perimeter = 28 – x + 4 + x + 24

Perimeter = 28 + 28 = 56

Hence, the perimeter of the triangle is 56 cm.