DS Section 16, #17

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jaheer: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Thu Feb 15, 2007 1:50 am

by jaheer » Mon Feb 19, 2007 6:38 am

17. The figure above shows the shape of a flower bed. If arc QR is a semicircle and PQRS is a rectangle with QR > RS, what is the perimeter of the flower bed ?
(1) The perimeter of rectangle PQRS is 28 feet.
(2) Each diagonal of rectangle PQRS is 10 feet long.

I've attached the picture. It is a rectangle PQRS with Semi-circle on the top.

I feel the answer is B, but correct answer mentioned is C. Can someone please explain.

Thanks in Advance.
Jaheer

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Source: Beat The GMAT — Data Sufficiency | Mon Feb 19, 2007 6:38 am

Vasudha: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Fri Jan 12, 2007 3:24 am; Location: Notre Dame; Thanked: 1 times

by Vasudha » Sun Mar 11, 2007 7:07 pm

Hi

I dont see the attached image ..

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jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pmFollowed by: 1 member; Location: Silicon valley, California; Thanked: 30 times

by jayhawk2001 » Sun Mar 11, 2007 8:20 pm

I can't find the image but given that we have the semicircle on top of
the rectange, lets assume

PS = QR = l
RS = QP = w

We should find l and w to solve this.

1 - insufficient. All we know is 2(l + w) = 28

2 - insufficient. All we know is l^2 + w^2 = 100. Cannot solve for l or w.

Using 1 and 2, we have 2 equations with 2 variables. So, a solution
should exist and hence is sufficient.

Sub l = 14 - w

196 + w^2 - 28w + w^2 = 100
w^2 - 14w + 48 = 0
w = 8 or 6

We are given that l > w and so we know what l is. Perimeter of the
flower-bed can hence be computed.

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Vasudha: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Fri Jan 12, 2007 3:24 am; Location: Notre Dame; Thanked: 1 times

by Vasudha » Sun Mar 11, 2007 8:50 pm

Thank you, jayhawk2001.

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