Question

Find the height, x, of the triangle. A. 30 B. 40 C. 50 D. 60

Answer 1

The correct option is;

A. 30

Explanation:

Given that the perpendicular bisector forms two other right angled triangles, we have;

For the larger right angled triangle, hypotenuse length = 100

For the smaller right angled triangle, hypotenuse length = 90

We note that;

y² = x² + 10²

z² = x² + 90²

100² = z² + y ²

Therefore we have;

100² = x² + 10² + z² = x² + 10² + x² + 90² = 2·x² + 90² + 10²

10000 = 2·x² + 8200

2·x² = 10000 - 8200 = 1800

x² = 1800/2 = 900

x = 30