In a right-angled triangle, the hypotenuse is 4 cm larger than one of the legs.

In a right-angled triangle, the hypotenuse is 4 cm larger than one of the legs. Determine the median drawn to the hypotenuse if the other leg is 8 cm.

1. AC = 8 cm – leg of a right-angled triangle ABC. ∠А = 90 °. The hypotenuse BC is greater than the leg
AB by 4 cm. AE – median.
2. To solve the problem, we use the Pythagorean theorem:
AB² + AC² = BC².
4. Take the length of the leg AB as x. The length of the hypotenuse BC – (x + 4):
x² + 8² = (x + 4) ²;
x² + 64 = x² + 8x + 16;
8x = 48;
x = 6 cm.
AB = 6 cm.
BC = 6 + 4 = 10 cm.
5. According to the properties of the rectangle, the median drawn from the vertex of the right angle
is equal to 1/2 hypotenuse:
AE = 10: 2 = 5 cm.
Answer: median AE = 5 cm.