Assuming x represents the length of the first side.
Use pythagorean theorem to solve:
<span>a^2</span> + <span>b^2</span> = <span>c^2</span>
<span>x^2</span> + <span><span>(x+7)^</span>2</span> = <span>13^2</span>
<span>x^2</span> + <span><span>x^2</span>+14x+49</span> = 169
<span>2<span>x^2</span></span> + 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 = <span>b<span>h/2</span></span>
A = <span><span>b<span>(h)</span></span>2</span>
A= <span><span>12<span>(5)</span></span>2</span>
A = <span>30c<span>m^<span>2</span></span></span>
