Problema Solution
A toy manufacturer needs a piece of plastic in the shape of a right triangle with the lower leg 7 cm more than the shorter leg and the hypotenuse 14 cm more than the shorter leg. How long should the sides of the triangle be?
Answer provided by our tutors
let
'a' and 'b' represent the legs of the right triangle and 'a' is the lower leg, 'b' the shorter leg
'c' represent the hypotenuse
a, b and c are positive numbers
the lower leg is 7 cm more than the shorter leg means:
a = 7 + b
the hypotenuse is 14 cm more than the shorter leg:
c = 14 + b
by the Pythagorean Theorem we know:
a^2 + b^2 = c^2
plug a = 7 + b and c = 14 + b into the last equation:
(7 + b)^2 + b^2 = (14 + b)^2
by solving we find:
b = 21 cm
click here to see the step by step solution of the equation:
a = 7 + 21
a = 28 cm
c = 14 + b
c = 14 + 21
c = 35 cm
the sides of the triangle are: the legs are 28 cm and 21 cm, the hypotenuse is 35 cm.