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DS Geometry questions

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by sanaa.rizwan » Mon Apr 29, 2013 11:03 am
what is the area of the rectangular region R?

1.each diagnosis of R has length 5
2.the perimeter of R id 14

In statement 1

length of diagonal of rectangle = hypotenuse of a 30-60-90 triangle
if we know one side of a right triangle we can find the length of other 2 sides, what would be the length and height of the rectangle, hence area can be determined.
so statement 1 is SUFFICIENT

but the answer to this question is C. How is statement 1 is NOT SUFFICIENT
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by Anju@Gurome » Mon Apr 29, 2013 11:18 am
sanaa.rizwan wrote:length of diagonal of rectangle = hypotenuse of a 30-60-90 triangle
The triangle can very well be 45-45-90 triangle or 20-70-90 triangle or 40-50-90 triangle. In each case the lengths of the sides will be different and the address of the rectangular region will be different too.
sanaa.rizwan wrote:what is the area of the rectangular region R?

1.each diagnosis of R has length 5
2.the perimeter of R id 14
Let us assume the lengths of the two sides of the rectangular region is a and b.
Hence, area of the region = ab

Statement 1: a² + b² = 5² = 25
This is not enough to determine the value of ab.

Not sufficient

Statement 2: 2(a + b) = 14 ---> (a + b) = 14
This is not enough to determine the value of ab.

Not sufficient

1 & 2 Together: Now we can determine the value of ab as (a + b)² = a² + b² + 2ab
So, ab = [(a + b)² - a² - b²]/2

Sufficient

The correct answer is C.
Last edited by Anju@Gurome on Mon Apr 29, 2013 11:39 am, edited 1 time in total.
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by srcc25anu » Mon Apr 29, 2013 11:25 am
From 1 we know diagonal = 5
But it can be a square (Sqaure is a special rectangle with all sides equal) and in that case area will be 25 / 2 or 12.5
but if diagonal = 5 and sides of recatngle are 4 and 3, then area will be 12
hence Insufficient

From 2 we know Perimeter = 14
again if we assume a sqaure, each side = 14/4 or 3.5 and area will be 3.5^2 = 12.25
but if we assume a rectangle with side 3 and 4, area will be 12
Not sufficient

Together: we know diagonal = 5 and sum of L + B = 7 (since P =14)
thus it has to be a 3*4 rectangle as diag^2 = L^2 + B^2
Area = 3 * 4 = 12
Sufficient. Ans C
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by sanaa.rizwan » Mon Apr 29, 2013 11:36 am
I understand what you mean, the diagonal make a rectangle into a 2 right triangles but not necessarily a 30-60-90 or 45-45-90

Also can you explain how did you come with the area of the square to be 12.5 given the length of diagonal = 5

Thanks a lot
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by Blue_Skies » Mon Apr 29, 2013 2:46 pm
what is the area of the rectangular region R?

1.each diagnosis of R has length 5
2.the perimeter of R id 14

What do you need to find area of a rectangle ? L X B .
With a given diagonal we can adjust L x B and make many rectangles. Hence 1 is Out.
Now perimeter=2(L+B)=14 -> L+B=7.
Now if we know the perimeter and the diagonal than we can find area because we know :

(L+B)square = l2+B2+2LB = 49.
from pythogorus theorm we know l2+b2 = 25. So we can subsitute that above and get 2LB which gives us the area. Hence C is tha answer.
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