Answer:
Here
Step-by-step explanation:
The longer leg of a right triangle is 7 cm longer than the shorter leg. The hypotenuse is 8 cm longer than the shorter leg. What is the perimeter of the triangle?
Let the shorter leg =x
So longer leg = x+7
Hypotenuse =x+8
Now, by pythagoras theorem
x^2+(x+7)^2=(x+8)^2
x^2 + x^2+14x+49=x^2+16x+64
x^2–2x–15=0
this is a quadratic equation
(x-5)(x+3)=0
x=5 & -3
-3 can't be a side.
so shorter side=5, longer side=12, hypotenuse=13.
Perimeter of triangle = 5+12+13=30.
Alternate method-
If you know the triplets (5,12,13) in which longer side is 7 more than shorter side and hypotenuse is 8 more than the shorter side.
So these are the sides of the triangle which satisfies the given condition.
