# Given the hypothenuse of right triangle of 26 cm long and one cathetus 14 cm longer than the other , what are the lengths of the legs of triangle.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll note:

a = shorter leg
b = longer leg
c = hypothenuse

We'll apply Pythagorean Theorem in the given right triangle:

c^2 = a^2 + b^2

But b is 14 cm longer than a. We'll write the phrase mathematically:

b  = a + 14

We'll re-write Pythagorean Theorem:

c^2 = a^2 + ( a + 14)^2

But c = 26. We'll substitute c in the Pythagorean Theorem and we'll expand the square:

26^2 = a^2 + a^2 + 28a + 196

We'll combine like terms:

676 = 2a^2 + 28a + 196

We'll divide by 2:

a^2 + 14a + 98 - 338 = 0

We'll combine like terms:

a^2 + 14a- 240 = 0

a1 = [-14+sqrt(196 + 960)]/2

a1 = (-14+34)/2

a1 = 10

a2 = (-14-34)/2

a2 = -24

Since we are talking about a distance, which is always positive, we'll reject a2 = -24.

One leg of triangle will have the length a = 10 cm and the other leg, b = 14 + 10:

b = 24 cm