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

A right triangle has the leg lengths of 3X and 40

Ответ:

GingerSnaps

22.01.2022

Mathematics

Hypotenuse = 10 units

Step-by-step explanation:

According to the Pythagoras theorem:

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