In an isosceles right-angled triangle, the hypotenuse and the height drawn

In an isosceles right-angled triangle, the hypotenuse and the height drawn to the hypotenuse add up to 27 cm. Calculate the height of the triangle.

1. A, B, C – the vertices of the triangle. AE – height. ∠А = 90 °. AE + BC = 27 centimeters.

2. By the condition of the problem, ΔАВС is isosceles. Therefore, the height AE is also the median.

3. The median drawn from the vertex of the right angle to the hypotenuse is equal to 1/2 of the hypotenuse (according to the properties of a right-angled triangle).

Therefore, BC = 2AE.

4. AE + BC = 27 centimeters. We substitute here 2AE instead of BC:

AE + 2AE = 27 centimeters.

3AE = 27 centimeters.

AE = 9 centimeters.

Answer: The height of AE is 9 centimeters.