The height of a right-angled triangle, drawn from the top of the right angle, divides the hypotenuse

The height of a right-angled triangle, drawn from the top of the right angle, divides the hypotenuse into segments, one of which is 11 cm larger than the other. Find the hypotenuse if the legs of the triangle are 6: 5.

The height of a right-angled triangle, drawn from the apex of the right angle, divides the original triangle into two similar right-angled triangles.

The legs of the original triangle are the hypotenuses of the two resulting triangles, and the ratio is 6: 5. And each of the segments of the hypotenuse is the legs of two triangles. Let the smaller segment of the hypotenuse be “X”, then the larger one will be “X + 11”. By the property of similarity of triangles, we write the ratio:

(X + 11) / X = 6/5;

5X + 55 = 6X;

X = 55 (cm).

Let’s find the hypotenuse:

X + (X + 11) = 55 + (55 + 11) = 121 (cm).

Answer: The hypotenuse of the triangle is 121 cm.