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# A rhombus PQRS has A, B, C, D as mid points of its sides PQ, QR, RS an

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A rhombus PQRS has A, B, C, D as mid points of its sides PQ, QR, RS an  [#permalink]

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15 Aug 2018, 10:21
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00:00

Difficulty:

95% (hard)

Question Stats:

50% (02:36) correct 50% (01:47) wrong based on 46 sessions

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A rhombus PQRS has A, B, C, D as mid points of its sides PQ, QR, RS and SP respectively. A, B, C, D are joined to form quadrilateral ABCD. What is the perimeter of quadrilateral ABCD?

(1) PQ = 10 units.

(2) PR = 16 units.
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A rhombus PQRS has A, B, C, D as mid points of its sides PQ, QR, RS an  [#permalink]

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15 Aug 2018, 11:36
1
amanvermagmat wrote:
A rhombus PQRS has A, B, C, D as mid points of its sides PQ, QR, RS and SP respectively. A, B, C, D are joined to form quadrilateral ABCD. What is the perimeter of quadrilateral ABCD?

(1) PQ = 10 units.

(2) PR = 16 units.

ABCD is a rectangle. (When we joint the midpoints of a rhombus , a rectangle emerges)

Rephrased question stem:- What is the perimeter of the rectangle ABCD?
a) Length & breadth , both required

St1:- PQ = 10 units
We can only determine the diagonals of the rectangle. PQ=BD=10=PS=AC.
Not sufficient to determine length & breadth of the rectangle.

St2:- PR = 16 units

In the triangle QRP, AB || PR and A & B are the midpoints of two of it's sides , so $$AB=\frac{PR}{2}=\frac{16}{2}$$=8 units=breadth of rectangle.

There is no sufficient info to determine the length of rectangle, BC.

Combining, we have, in the right angled triangle ABC, AC=diagonal=10 units(from st1) and AB=8 units (from st2)

So, $$BC=\sqrt{10^2-8^2}$$=6 units

Now perimeter can be determined using the formula: P=2(AB+BC)
Sufficient.

Ans. (C)
Attachments

Rectangle.JPG [ 23.6 KiB | Viewed 301 times ]

_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

A rhombus PQRS has A, B, C, D as mid points of its sides PQ, QR, RS an &nbs [#permalink] 15 Aug 2018, 11:36
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