The leg of a right-angled triangle is 6 cm, and its projection onto the hypotenuse is 4 cm. Find the hypotenuse.

We are given a right-angled triangle. His leg is known – 6 cm, and his projection onto the hypotenuse is also known – 4 cm. It remains to find the hypotenuse.

To solve the problem, we will apply the following property of the leg and its projection onto the hypotenuse in a right-angled triangle.

So, the leg of a right-angled triangle is the average proportional between the hypotenuse and its projection onto the hypotenuse. We write it in the form of a formula:

a ^ 2 = c * ac;

Where c is the hypotenuse, a is the leg, and ac is the projection of the leg onto the hypotenuse.

Substitute the values and calculate:

6 ^ 2 = 4 * c;

4c = 36;

c = 36: 4;

c = 9 cm.