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?

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Answer 1 · 2015-12-27T15:45:39

Draw a diagram to represent the question:

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Assuming x represents the length of the first side.

#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#