Question

The length of one leg of a right triangle is 7 cm more than that of the other leg. The length of the hypotenuse is 3 cm more than double that of the shorter leg. Find the lengthzs of each of the three sides.

Answer 1

Answer:

The lengths are 5, 12, and 13.

Step-by-step explanation:

Let x represent the shorter leg of the triangle. Since the other leg is 7 cm more, the longer leg is x+7. Since the length of the hypotenuse is 3 cm more than double that of the shorter leg, the hypotenuse is 2x+3.

The Pythagorean Theorem may be used to find the lengths.

$a^{2}$ + $b^{2}$ = $c^{2}$  a, b are the short and long lengths and c is the hypotenuse

→ $x^{2} + (x+7)^{2} = (2x+3)^{2}$

→ $x^{2} + x^{2} + 14x + 49 = 4x^{2} + 12x + 9$

→ $2x^{2} + 14x + 49 = 4x^{2} + 12x + 9$

→ $2x^{2} - 2x - 40 = 0$

→ $x^{2} - x - 20 = 0$

→ $(x-5)(x+4) = 0$

→ $x = 5$ (The length cannot be negative)

The shorter leg, x, is 5 cm. Since the longer leg is x+7, it is 12 cm. Since the length of the hypotenuse is 2x+3, the hypotenuse is 13 cm.