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?

Draw a diagram to represent the question:

Assuming x represents the length of the first side.

Use to solve:

##a^2## + ##b^2## = ##c^2##

##x^2## + ##(x + 7)^2## = ##13^2##

##x^2## + ##x^2 + 14x + 49## = 169

##2x^2## + 14x - 120 = 0

Solve the quadratic equation using the quadratic formula.

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(h) / 2##

A = ##{b(h)} / 2##

A= ##{12(5)} / 2 ##

A = ##30 cm^2##