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Geometry

by anksbhandari » Mon Aug 04, 2008 7:20 am
In the diagram to the right, triangle PQR has a right angle at Q and a perimeter of 60. Line segment QS is perpendicular to PR and has a length of 12. PQ > QR. What is the ratio of the area of triangle PQS to the area of triangle RQS?


3/2

7/4

15/8

16/9

2
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by pepeprepa » Mon Aug 04, 2008 8:33 am
would say E
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by sudhir3127 » Mon Aug 04, 2008 9:02 am
My answer is D.

a^2 + b^2 = c^2 Pythagorean Theorem for right triangle PQR

ab/2 = 12c/2 ( 1/2 *b*h ... (assuming a and b are lengths of PQ and QR and C is hypoteneuse PR)

now we now a^2 +b^2 = c^2
(a + b)^2 = (a^2 + b^2) + 2ab
(a + b)^2 = c^2 + 24c
(60 – c)^2 = c^2 + 24c ( since a +b+c = 60)

solve this to get C = 25, a= 20 and b = 15.

Rule : the height of the hypotenuese divides the right triangle into 2 smillar triangles.

there fore the ratio of the areas would be (20/15)^2 which 16/9

hope its clear... let me know if u have any doubts..
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Another way

by anksbhandari » Mon Aug 04, 2008 10:38 am
Sudir Your expl is right , just see this one also.

Pythagoras theorem a traingle can be in the ration of : 3,4,5 or 5,12,13

Add: 3+4+5 = 15
or 5+12+13 = 30

Perimeter is 60, therefore side can be: 15, 20, 25 or 10 , 24, 36

Now side PQ > PR, therefore Side PQ can be 20 or 24
and side PR can be 15 or 10

Ratio of Area of similar triangle A/ Area of similar triangle B = Side A^2/ Side B^2

Ratio of PQS/ RQS = 20^2/15^2 = 16/9 or

24^2/10^2 = 576/100

Since, 16/9 is the option given, therefore, answer is D

this solution will not take more than 1 minute.
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by jimmytwoshoes » Sat Aug 09, 2008 10:26 am
Add: 3+4+5 = 15
or 5+12+13 = 30


You mean that 3+4+5 = 12, correct?
(still a divisor of 60)
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