A triangle has a base of 8 inches and sides of 3 and 6 inches. What is the height of the triangle? Round to the nearest hundredth.

Question

Answer: The height is approximately ____________in.

Answer 1

Area A = [s(s - a)(s- b)(s - c)]^1/2, where s = (8 + 3 + 6)/2 = 8.5;

A = (8.5·0.5·2.5·5.5)^1/2 = √935/4

A = 0.5hb = 4h; 4h = √935/4; h = √935/16 = 1.91

Answer 2

Yefim, as always, has a great solution. I wanted to provide an alternate solution.

If you draw the triangle, you can see the altitude a that we are solving for, the base of length 8 separated into two parts x and 8-x, and the hypotenuses of length 3 and 6 of these two right triangles made up of the altitude, the two different parts of the base, and these hypotenuses.

Thus, x^2 + a^2 = 3^2 = 9

(8-x)^2 + a^2 = 6^2

x^2 - 16x + 64 + a^2 = 36

Subtracting the left and right hand sides,

-16x + 64 = 27

-16x = -37

x = 37/16

Then, x^2 + a^2 = 9

1369/256 + a^2 = 9

a^2 = 935/256

a = √935/16