Question

I NEED ANSWER ASAP! I WILL GIVE BRAINELIEST!!!!!! Construct a right triangle whose legs are in the ratio 3:4. What are the ratios of each leg to the hypotenuse? I NEED IN RATIO FORM PLZ HELP!!!!!!!​

Answer 1

Answer:

3 : 5, 4: 5

Step-by-step explanation:

Let the common multiplier of the given ratios be x.

Therefore, lengths of the legs of right triangle would be 3x and 4x

By Pythagoras Theorem:

${hyp}^{2} = {(3x)}^{2} + {(4x)}^{2} \\ = 9 {x}^{2} + 16 {x}^{2} \\ = 25 {x}^{2} \\ hyp = \sqrt{25 {x}^{2} } \\ hyp = 5x \\ \\ ratios \: of each \: leg \: to \: the \: hypotenuse \\ \frac{3x}{5x} = 3 : 5 \\ \\ \frac{4x}{5x} = 4 : 5$