Use the Pythagorean theorem to find the lengths of the sides of the right triangle. Use a calculator when necessary. A right triangle has legs labeled 3m and 2m+10 and a hypotenuse labeled 5m. 3m 5m 2m+10

The length of the sides of the right angle triangle

15 , 25, 20

Step-by-step explanation:

Explanation:-

Step(i):-

we know that by using Pythagorean theorem to find the lengths of the sides of the triangle

AC² = AB² + BC²

Given a  right triangle has legs labeled 3m and 2m+10

let us assume that AB = 3m and BC = 2m + 10

Given a hypotenuse  labeled 5m

let us assume that hypotenuse AC = 5m

Step(ii):-

Now by using Pythagorean theorem

AC² = AB² + BC²

(5m)² = (3m)² + (2m+10)²

25m² = 9m² + 4m² + 40m + (10)²  ( since (a + b)² = a²+2ab+b²) )

on simplification , we get

25m²-13m² -40m -100 =0

12m² -40m -100 =0

4(3m² -10m -25) =0

3m² -10m -25 =0

3m² - 15m + 5m -25 =0

3m(m-5) + 5(m-5) =0

(3m +5) (m-5) =0

3m +5 =0 and m-5=0

3m = -5 and m =5

and m=5

we can not choose negative value

so the value m=5

Step (iii):-

The sides of right angle triangle

AB = 3m

AB = 3(5) = 15 and

BC = 2m + 10

BC = 2(5) +10 = 20

The hypotenuse AC =  5m

                           AC = 25

Conclusion:-

The  lengths of the sides of the right triangle

15, 25 ,20