Question

The hypotenuse of a 45°, 45°, and 90° triangle is 26 sqrt(2) inches. What is the length of each of the other sides?

(A)13 sqrt(2) inches
(B)13 inches
(C)13 sqrt(3) inches
(D)26 inches

Answer 1

remember the pythagorean theorem:

a² + b² = c²

where c is the hypotenuse.

so:

`{a}^(2) + {b}^(2) = { ( √(26))}^(2)`

the square and the square root cancel each other out, so...

a² + b² = 26

we know that a and b are of equal length given the angles.

so it's

`{ √(13) }^(2) + { √(13) }^(2) = 26`

here the squares and square roots also cancel, but to keep the equation from the formula true we need to write them. that makes the difference between optional and B

Option A is correct,

`√(13) inches`