Answer:
The length of the sides of the right angle triangle
15 , 25, 20
Step-by-step explanation:
<u>Explanation</u>:-
<u>Step(i):-</u>
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
<u>Step(ii)</u>:-
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
<u>Step (iii)</u>:-
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
<u>Conclusion:</u>-
The lengths of the sides of the right triangle
15, 25 ,20