surface area of a rectangular pool

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apshara5: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Sun Nov 14, 2010 8:08 am

by apshara5 » Wed Oct 19, 2011 2:34 pm

Is the surface area of a rectangular pool lager than 1000 square feet.
1 the pool measure fifty feet diagonally
2 one side of the pool side measure 25 feet
ans :c

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Source: Beat The GMAT — Data Sufficiency | Wed Oct 19, 2011 2:34 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Oct 20, 2011 1:08 am

apshara5 wrote:Is the surface area of a rectangular pool lager than 1000 square feet.
1 the pool measure fifty feet diagonally
2 one side of the pool side measure 25 feet

To determine the surface area of the rectangular pool we need the measures of two consecutive sides of the pool. None of the statements individually provide the required information.

But both statements together, we know length of the diagonal, d = 50 feet and measure of one side, a = 25 feet.

Hence, we can find the measure of the other side, b as follows,

b = âˆš(dÂ² - aÂ²)

Hence, required surface area = a*b = a*(âˆš(dÂ² - aÂ²))
As we know a and d, we can calculate the area

The correct answer is C.

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Thu Oct 20, 2011 1:13 am

A rectangular pool can be considered as a box(cuboid)

The SA of a cuboid is 2(LB+BH+HL)

(1) Diagonal measures 50.
Now the diagonal can be that of LB,BH or HL.

We can have 2 sides as say 35,35 where SA is > 1000
or we have a side measuring more than 49 and the other 1, where the SA<1000.

We can't say.

(B) only one side is given and obviously we can have both the cases possible.

Combined: We know one diagonal measures 50 and a side is 25. So the SA will be greater than 1000.

Hence C

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Thu Oct 20, 2011 1:23 am

Is surface are > 1000 ?

1) Diagonal = 50ft.

Say, a,b are the sides of the rectangle => a^2 + b^2 = 50^2 [spoiler]so 2(a+b) = ? Insufficient [/spoiler]

2)One side of the pool side measure 25 feet

Say a,b are the sides of the rectangle => 25^2 + b^2 = c^2 [spoiler]so 2(a+b) = ? Insufficient [/spoiler]

Using 1 and 2 [spoiler]a =25, c=50, b =25 square(3) Hence option C[/spoiler]

Anil Gandham
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