marcusaurelius wrote:

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.

I know that (2) is sufficient but I am having difficulty with (1).

The best approach to tackle statement questions in DS is as follows:

Step 1: Convert all the alphabetical statements in algebraic statements

Step 2: Reduce the number of variable to minimum

Step 3: Check how many variables are left. You may probably need that many statements to solve the questions but you might need lesser number of statements to answer the question.

Caution: Don't waste your time in solving the question. You have to analyse the data sufficiency and not solve the question.Lets see how this approach works for this question:

Step 1: A right triangle is given with hypotenuses equal 10. A triangle has three side. Let the other two sides be a and b

We know in a right triangle a^2 + b^2 =100

and we have to determine perimeter = a + b + 10

Step 2: We introduced 2 variables a and b above. Can we reduce the constraint equation to one variable. Yes, we can.

p = a + \sqrt{100-a^2} + 10

Thus, we are left with one variable.

Step 3: Let us look at the statements and see if we can decipher this one variable

1) The area of the triangle is 25 square centimeters.

Area of a right triangle is 1/2*a*b = 25

But we know the relationship between a and b as well. Therefore, we can calculate a and hence perimeter. Thus, this is a sufficient condition.\

2) The 2 legs of the triangle are of equal length.

This means a= b

Again, we can calculate a here and thus can find out the perimeter. Again sufficient.

Thus, the correct answer is D.

Note: We didn't solve for a or p nor did we enter any algebra here