Answer:
The lengths of the sides are 5, 12, 13.
Step-by-step explanation:
In a right triangle, the two shorter sides are the legs. The longest side is the hypotenuse.
Let the shorter leg = x.
The longer leg is 7 cm longer, so its length is x + 7.
The length of the hypotenuse is 8 cm longer than the shorter leg, so its length is x + 8.
The lengths are:
x, x + 7, x + 8
Since the triangle is a right triangle, we can use the Pythagorean theorem.
a^2 + b^2 = c^2
x^2 + (x + 7)^2 = (x + 8)^2
Square the trinomials.
x^2 + x^2 + 14x + 49 = x^2 + 16x + 64
Combine like terms and place them all on the left side equaling zero.
x^2 - 2x - 15 = 0
Factor the left side.
(x - 5)(x + 3) = 0
x - 5 = 0 or x + 3 = 0
x = 5 or x = -3
Since the length of a side of a triangle cannot be negative, we discard the solution x = -3.
x = 5
x + 7 = 5 + 7 = 12
x + 8 = 5 + 8 = 13
Answer: The lengths of the sides are 5, 12, 13.
