Question

select all the correct answers.
asher cut five sets of boards to build triangular tables. which of the following sets of side lengths would form tables shaped like a right triangle?
28 in, 45 in, 53 in
20 in, 21 in, 31 in
18 in, 22 in, 28 in
27 in, 36 in, 45 in
10 in, 24 in, 26 in

Explanation:

Step1: Check Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, where $c$ is the longest side.

Set1: 28 in, 45 in, 53 in

Calculate $28^2 + 45^2 = 784 + 2025 = 2809$, $53^2 = 2809$.

Set2: 20 in, 21 in, 31 in

Calculate $20^2 + 21^2 = 400 + 441 = 841$, $31^2 = 961$.

Set3: 18 in, 22 in, 28 in

Calculate $18^2 + 22^2 = 324 + 484 = 808$, $28^2 = 784$.

Set4: 27 in, 36 in, 45 in

Calculate $27^2 + 36^2 = 729 + 1296 = 2025$, $45^2 = 2025$.

Set5: 10 in, 24 in, 26 in

Calculate $10^2 + 24^2 = 100 + 576 = 676$, $26^2 = 676$.

Step2: Identify valid sets

Match where $a^2 + b^2 = c^2$.

Answer:

28 in, 45 in, 53 in
27 in, 36 in, 45 in
10 in, 24 in, 26 in