We have a triangle triangle ABC and a point K on BC such that AK is an altitude to triangle ABC. If AC = 10, BK = 7, and BC = 14, then what is the area of triangle ABC?

Guest Feb 19, 2022

#1**+1 **

Since BC = 14 and BK = 7, CK = 7.

Since AK is an altitude, triangle(AKC) is a right triangle with hypotenuse AC.

Using the Pythagorean Theorem: AK^{2} + KC^{2} = AC^{2}.

---> AK^{2} + 7^{2} = 10^{2}

Find the value of AK.

The height of the triangle is AK and the base is BC.

Since you know these two values, you can find the area of the triangle.

geno3141 Feb 19, 2022