In the given diagram, PQU is an equilateral triangle, QRVU is a square and RSTU is a parallelogram. Find the perimeter, (in cm) of the whole diagram.

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26 + 4 \sqrt{2}

20 + 8 \sqrt{2}

26 + 8 \sqrt{2}

25 + 8 \sqrt{2}

answer is C.

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Detailed Solution

Given PQU is triangle with equal sides (equilateral triangle).
Thus,

PQ = PU = QU = 4 cm

In the figure we have QUVR is a square as well. So all sides of it will be equal. So,

QU = UV = VR = QR = 4 cm

Now, RUTS is a parallelogram. Here, opposite sides will be equal. So,

UT = SR = 5 cm

Now we know that,
Diagonal of square QUVR,

RU = \sqrt{2} \times (side)

RU = \sqrt{2} \times (4)

RU = 4 \sqrt{2}

cm
So,

RU = ST = 4 \sqrt{2} cm

(opposite sides of parallelogram)
Now, needed perimeter

= PU + UT + TS + SR + QR + PQ

= (4 + 4 + 5 + 5 + 4 + 4 + 4 \sqrt{2} + 4 \sqrt{2}) cm

= 26 + 8 \sqrt{2} cm

Correct option is 3.

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