In triangle XYZ, XZ=7, YZ=7, and XY=6. What is the area of the triangle in simplified radical form?
Let XY be the base and XZ and YZ be the sides
Using the Pythagorean Theorem we can find the height as
√[ YZ^2- (XY/2)^2 ] = √ [ 7^2 - (3)^2 ] = √[49 - 9] = √40 = 2√10
So...the area = (1/2)(XY) (height) = (1/2)(6) (2√10) = 3 (2√10) = 6√10 [units^2]
