Find the lengths of the legs of a right-angled triangle, if the height of the triangle, drawn from the top of the right angle

Find the lengths of the legs of a right-angled triangle, if the height of the triangle, drawn from the top of the right angle, divides the hypotenuse into 2 segments 8cm and 10cm long.

We know the lengths of the segments into which the height, lowered from the right angle, divides the hypotenuse. Find the hypotenuse by adding the lengths of the line segments.

s = 8 cm + 10 cm = 18 cm.

Let’s calculate the length of the first leg.

a = √ (18 cm * 8 cm) = 12 cm.

Now we find out the length of the second leg.

b = √ (18 cm * 10 cm) = 13.4 cm.

Answer: the legs are 12 cm and 13.4 cm.