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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DS Section 16, #17
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jayhawk2001
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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.
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.
