Carcass wrote:

What are the lengths of sides NO and OP in triangle NOP below?

Attachment:

#GREexcecise What are the lengths of sides NO and OP in triangle NOP below.jpg

\(NO = 30\) and \(OP = 10 \sqrt{34}\)

Let's add some more angles to the diagram AND also....

...add labels for points

L and

MAt this point, we can see that there are TWO

SIMILAR triangles hiding in this diagram.

So, let's draw them apart to get a better idea of these two triangles:

What is the length of side NO?KEEP CONCEPT: With any two SIMILAR triangles, the

ratios of corresponding sides will be equal.

ON and LM are corresponding sides

Also, NP and MP are corresponding sides

Let x = the length of side NO

We can write: ON/LM = NP/MP

Replace values to get: x/24 = 50/40

Cross multiply: 40x = (24)(50)

Simplify: 40x = 1200

Solve: x = 1200/40 = 30

So,

side NO has length 30--------------------------------

What is the length of side OP?Now that we know NO has length 30, we can see that we know two sides of triangle NOP

Since NOP is a RIGHT triangle, we can apply the Pythagorean Theorem.

So, we can write: 30² + 50² = OP²

Simplify: 900 + 2500 = OP²

Simplify: 3400 = OP²

Solve: OP = √3400 = = 10√34

So,

side OP has length 10√34 Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

If you enjoy my solutions, you'll like my GRE prep course.

Sign up for GRE Question of the Day emails