Question

A right triangle has the leg lengths of 3X and 40 and a hypotenuse of length 5X. How long are the sides?

Answer 1

Hypotenuse = 10 units

Explanation:

According to the Pythagoras theorem:

`{hyp}^(2) = {(one \: leg) }^(2) + {(other \: leg)}^(2) \\ \therefore \: {(5x)}^(2) = {(3x)}^(2) + {40}^(2) \\ \therefore \: {25x}^(2) = {9x}^(2) + 1600 \\ \therefore \: {25x}^(2) - {9x}^(2)= 1600 \\ \therefore \: {16x}^(2)= 1600 \\ \therefore \: {x}^(2)= (1600)/(16) \\ \therefore \: {x}^(2)= 100 \\ \therefore \: {x}= 10 \\`

Hence, length of hypotenuse = 10 units.