Question

The hypotenuse of a right triangle is 10 cm. What is the perimeter, in centimeters, of the triangle?
(1) The area of the triangle is 25 square centimeters.
(2) The 2 legs of the triangle are of equal length.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is D Each statement alone is sufficient.

If x and y are the lengths of the legs of the triangle, then it is given that . To determine the value of x + y + 100, the perimeter of the triangle, is equivalent to determining the value of x + y.

1. Given that the area is 25, then , or xy = 50. Since, it follows that or ; SUFFICIENT.
2. Given that x = y, since , it follows that . Hence, x + y = x + x = 2x = ; SUFFICIENT.

• The correct answer is D; each statement alone is sufficient.