The longer leg of a right triangle is 2 centimeters longer than twice its shorter leg. The hypotenuse is 1 centimeter longer than longer leg. Find the dimensions of the lengths of the triangle.
A)3 cm, 4 cm, 5 cm
B)2 cm, 5 cm, 10 cm
C)10 cm, 17 cm, 18 cm
D)5 cm, 12 cm, 13 cm

Question

Quizplus · Accepted Answer

Using the given information, let the shorter leg be x cm. Then, the longer leg is 2x + 2 cm, and the hypotenuse is (2x + 2) + 1 = 2x + 3 cm. By the Pythagorean theorem, $x^2 + (2x + 2)^2 = (2x + 3)^2$. Solving this equation leads to x = 5 cm, making the sides 5 cm, 12 cm, and 13 cm, which matches option D.

The Longer Leg of a Right Triangle Is 2 Centimeters