2014-08-22 09:00:38

A certain right triangle has a perimeter of 30 and sides of x, (x - 7), and (x + 1). What is its area?

The correct answer is 30

Explanation: If the triangle has a perimeter of 30, the sum of its sides is 30. That means that x + (x - 7) + (x + 1) = 30. You can solve for x by simplifying that to 3x - 6 = 30. Add 1 to both sides to get 3x = 36. Divide both sides by 3 to get x = 12. This means that the sides of the triangle are 5, 12, and 13. Since it's a right triangle, it can be assumed that the side 13 is the hypotenuse and the two legs are 5 and 12. As the area of a triangle is 1/2 base x height, and as the legs are equivalent to the base and height in this case, the area of the triangle is 1/2 (5 x 12), or 1/2 of 60, which is 30.