The hypotenuse in a right triangle is 13 cm. of the other two sides one is 7 cm longer than the other determine the lengths of those two sides

Assuming x represents the length of the first side.

Use pythagorean theorem 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 = bh/2

A = b(h)2

A= 12(5)2

A = 30cm^2