# The hypotenuse of a right triangle is 13 cm. One of the legs is 7 cm longer than the other. How do you find the area of the triangle?

Dec 27, 2015

Draw a diagram to represent the question:

#### Explanation:

Assuming x represents the length of the first side.

Use pythagorean theorem to solve:

${a}^{2}$ + ${b}^{2}$ = ${c}^{2}$

${x}^{2}$ + ${\left(x + 7\right)}^{2}$ = ${13}^{2}$

${x}^{2}$ + ${x}^{2} + 14 x + 49$ = 169

$2 {x}^{2}$ + 14x - 120 = 0

At the end, you will get side lengths of #(-14 ± 34) / 4, or -12 and 5

SInce a negative triangle length is impossible, 5 is the value of x and 5 + 7 is the value of x + 7, which makes 12.

The formula for area of a right triangle is A = $b \frac{h}{2}$

A = $\frac{b \left(h\right)}{2}$

A= $\frac{12 \left(5\right)}{2}$

A = $30 c {m}^{2}$