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.

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

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

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

$2 x^{2}$ $2x^2$ + 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 = $b \frac{h}{2}$ $b(h) / 2$

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

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

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