Area of a triangle

Geometry Level 2

Three circles of radii 110, 140 and 220 are tangent to one another. What is the area of the triangle formed by joining the centers of the circles?

Give your answer to the nearest integer.


The answer is 39904.

View wiki
A Former Brilliant Member by A Former Brilliant Member

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Using Heron’s Formula

A = s ( s − a ) ( s − b ) ( s − c ) A = \sqrt{s(s-a)(s-b)(s-c)} ; where s s = semi-perimeter of the triangle, and a a , b b and c c are the side lengths of the triangle

s = a + b + c 2 = 250 + 330 + 360 2 = 470 s = \frac{a+b+c}{2} = \frac{250+330+360}{2} = 470

A = 470 ( 470 − 250 ) ( 470 − 330 ) ( 470 − 360 ) = 39904 A = \sqrt{470(470-250)(470-330)(470-360)} = 39904 square units

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Edwin Gray
Sep 10, 2018

Connecting the centers, we have a triangle with sides 250, 330, and 360. We use Herron's formula, A= sqrt(s(s - a)(s - b)(s - c)), where s = (1/2)(a + b + c) = 470.

So A = sqrt((470)(220)(110)9140)) = 39904.3. Ed Gray

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...