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
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