The hypotenuse of a right triangle is 2 cm longer than the longer leg. The shorter leg is 23 cm shorter than the longer leg. Find the length of the longer leg of the triangle.

Answer 1

Longer Leg Length = 35 centimeters

h = 2+x = 2 cm + longer leg of a right triangle

x = 23+y = 23 cm + shorter leg

h^2 = (2+x)^2 = x^2 + (x-23)^2

x^2 +4x + 4= x^2 +x^2 -46x + 23^2

4x +46x = x^2 +23^2 -4

x^2 -50x +525 = 0

x = 15 or 35 cm ignore 15, longer leg length = 35 centimeters

y = -8 or 12 = length of shorter leg

it's a 12 35 37 sided triangle

a Pythagorean Triple 12^2 + 35^2 = 37^2