The legs of a right-angled triangle are 5 and 12 cm, and the hypotenuse is 13 cm.

The legs of a right-angled triangle are 5 and 12 cm, and the hypotenuse is 13 cm. Find the distance from the middle of the hypothesis to the smaller leg.

Let’s designate the triangle ABC. Corner C straight. From point K – the middle of the hypotenuse AB, lower the KM perpendicular to the smaller leg AC. KM ǁ BC. When the sides of the corner intersect with parallel straight lines:

AK / AM = KВ / MС. If AK = KB, then AM = MC;

AM = AC: 2 = 5: 2 = 2.5 cm.

Consider the triangle AKM. AK = 13: 2 = 6.5 cm, AM = 2.5 cm.

KM ^ 2 = AK ^ 2 – AM ^ 2;

KM ^ 2 = 6.5 ^ 2 – 2.5 ^ 2 = 42.25 – 6.25 = 36;

KM = √36 = 6.

Answer: The distance from the middle of the hypotenuse to the smaller leg is 6 cm.