Question

Andrew claims that a wooden bookend in the shape of a 45°- 45°- 90° right triangle has side lengths of 9 in., 9 in., and 11 in. Is he correct?

Answer 1

No; if the sides of the right angle are 9 in. long each, then the hypotenuse would need to be over 12 in.

Explanation:

According to the Pythagorean Theorem
for a right triangle with sides `a, b, c` where `c` is the hypotenuse
`color(white)("XXX")c=sqrt(a^2+b^2)`

For the given non-hypotenuse sides:
`color(white)("XXX") c=sqrt(9^2+9^2) = sqrt(162) ~= 12.73`

but Andrew claims `c=11`