Question

The altitude to the hypotenuse of a right angled triangle is 8 cm. If the hypotenuse is 20 cm long, find the lenghs of the two segments of the hypotenuse

Answer 1

Let the two segments of the hypotenuse be x and y.
Using the Pythagorean theorem, we know that:
x^2 + 8^2 = y^2
and
y^2 + 8^2 = 20^2
Simplifying the second equation:
y^2 = 20^2 - 8^2
y^2 = 336
y = sqrt(336) = 4sqrt(21)
Now we can use the first equation to solve for x:
x^2 + 8^2 = (4sqrt(21))^2
x^2 + 64 = 336
x^2 = 272
x = sqrt(272) = 4sqrt(17)
Therefore, the lengths of the two segments of the hypotenuse are 4sqrt(17) cm and 4sqrt(21) cm.