Solve.
-The hypotenuse of a right triangle is 9 feet long. One leg of the triangle is 5 feet longer then the other leg. Find the perimeter of the triangle.
A) $( \sqrt { 137 } + 9 ) \mathrm { ft }$
B) $\left( \frac { 5 } { 2 } + \frac { \sqrt { 137 } } { 2 } \right) \mathrm { ft }$
C) $( \sqrt { 137 } - 9 ) \mathrm { ft }$
D) $\left( - \frac { 5 } { 2 } + \frac { \sqrt { 137 } } { 2 } \right) \mathrm { ft }$

Question

Quizplus · Accepted Answer

Using the Pythagorean theorem $a^2 + b^2 = c^2$, where $c = 9$ (the hypotenuse), and one leg is $a$ and the other leg is $a + 5$. Solving for $a$ gives $a^2 + (a+5)^2 = 9^2$, which simplifies to $2a^2 + 10a - 56 = 0$. Solving this quadratic equation for $a$ gives the lengths of the legs, and adding these lengths to the hypotenuse gives the perimeter. The correct calculation leads to the perimeter being $( \sqrt { 137 } + 9 ) \mathrm { ft }$, which matches choice A.

Solve -The Hypotenuse of a Right Triangle Is 9 Feet (137+9)ft( \sqrt { 137 } + 9 ) \mathrm { ft }(137​+9)ft

Solve
-The Hypotenuse of a Right Triangle Is 9 Feet $( \sqrt { 137 } + 9 ) \mathrm { ft }$