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##