Answer:
The perimeter of the triangle is 56 cm.
Step-by-step 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.
