SOLUTION: What is the radius of the largest circle that will fit inside a triangle that has two 15-inch sides and an 18-inch side?

Question 1158998: What is the radius of the largest circle that will fit inside a triangle that has two 15-inch
sides and an 18-inch side?
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.


The given triangle is isosceles with congruent lateral sides of 15 inches long
and the base of 18 inches.


The altitude of this triangle drawn to the 18-inches side, divide this triangle in two right-angled triangles.


This altitude is one leg of these triangles, while the other legs are 18/2 = 9 inches long.


From the Pythagorean theorem, the length of the altitude is   = 12 inches.


Then the area of the given triangle is   = 9*12 = 108 sq.inches.


Let the radius of the inscribed circle be r.


Now use the formula  

    area = 

for the triangle, where P is the perimeter P of the triangle   P = 15+15+12 = 42 inches.


The area of the triangle is 108 sq.inches.


Hence,  108 = ,  which gives

    r =  =  =  =  inches.   ANSWER

RELATED QUESTIONS
what is the largest diameter circle that will fit inside a regular pentagon with 2-inch... (answered by ikleyn)

Find the diameter of the circle that can be circumscribed around a triangle that has two... (answered by greenestamps,ikleyn)

A triangle has two 13-in sides and a 10-in side. The largest circle that fits inside this (answered by Charles3475)

A triangle has two 13-cm sides and a 10-cm side. The largest circle that fits inside this (answered by MathLover1)

A cubic box has inside dimensions of 10 by 10 by 10 inches. What is the longest pole of... (answered by ikleyn)

What is the radius of the largest ball that will fit into a box that has the inside... (answered by tommyt3rd)

How long are the sides of an equilateral triangle inside a one inch... (answered by Edwin McCravy)

There is a circle inside a triangle the bottom of the triangle is 240 kilometers, one... (answered by stanbon)

A circle is inscribed inside a square that has an area of 256 in squared. What is the... (answered by Stitch)