The hypotenuse of a right triangle is 10cm long. one of the triangle's legs is three times the length of the other leg. find the lengths of the three sides of the triangle. in case of non-integer answer(s), round your answer(s) to the nearest hundredth.

The lengths of the three sides are 10 cm, 9.49 cm and 3.16 cm

Step-by-step explanation:

Let

c ------> the length of the hypotenuse of a right triangle

x -----> the length of one leg

y -----> the length of the other leg

we know that

-----> equation A (Pythagoras Theorem)

----> equation B

-----> equation C

Substitute equation B and equation C in equation A and solve for y

Find the value of x

therefore

The lengths of the three sides are 10 cm, 9.49 cm and 3.16 cm

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

answer: x=60