Question

Solve for the missing side length in this triangle ​

Answer 1

10 and 24units

Explanation:

Pythagoras' Theorem

Pythagoras' Theorem applies to right angle triangles with the formula:

`{c}^(2) = {a}^(2) + {b}^(2)`

where c is the longest side, with a and b the shorter ones (interchangable)

Solution

With the parameters given from the question and the formula given as well, we can find the value of x and therefore the side lengths.

By Pythagoras' Theorem,

`{26}^(2) = ( {5x)}^(2) + ( {12x)}^(2) \\ 676 = 25 {x}^(2) + 144 {x}^(2) \\ 169 {x}^(2) = 676 \\ {x}^(2) = 676 / 169 \\ {x}^(2) = 4 \\ x = √(4) \\ = 2`

Now we can find the side lengths.

`5x = 5(2) = 10units \\ 12x = 12(2) = 24units`

Therefore the side lengths are 10 and 24 units.