In the given Fig. ∆PQR ~ ∆MNS if PQ = 2 MN and area of ∆

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Triangles

Long Answer Type

351. In ∆PQR, ∠QPR = 90° and PM is perpendicular to QR. Prove that
(i)

increment PQM space tilde increment RQP

(ii)

PQ over QR equals QM over PQ

(iii)

increment PMR tilde increment QPR

(iv)

PR squared space equals space QR cross times MR.

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352.

In the given Fig., $OA over OC equals OD over OB.$ Prove that ∠A= ∠C and ∠B = ∠D.

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353. In the given AB || CD || EF. If AB = 6 cm, CD = x cm, EF = 10 cm, BD = 4 cm and DE = y cm, calculate the values of x and y.

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354.

In the given Fig., ∆ABC and ∆PQR are isoscles triangles in which ∠A = ∠P.
if $fraction numerator area space of space left parenthesis increment ABC right parenthesis over denominator area space of space left parenthesis increment PQR right parenthesis end fraction equals 9 over 16 comma$ find $AD over PS.$

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Short Answer Type

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355. In the given Fig. ∆PQR ~ ∆MNS if PQ = 2 MN and area of ∆PQR is 56 sq. cm, find the area of ∆DEF.

Solution not provided.
Ans. 14 sq.cm.

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Long Answer Type

356. ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, BP = 3 cm, AQ = 1.5 cm, CQ = 4.5 cm.
Prove that the area of

increment APQ space equals space 1 over 16 left parenthesis area space of space increment ABC right parenthesis.

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357.

In the given Fig. LM || NQ and LN || PQ. If $MP space equals space 1 third MN.$ Find the ratio of the areas of ∆LMN and ∆QNP.

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Short Answer Type

358. The areas of two similar triangles ABC and DEF are 64 cm² and 121 cm²respectively. If EF = 13.2 cm, find BC.

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Long Answer Type

359. In ∆ABC, PQ||AB and

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Find:

(i) area of ∆CPQ, if ar(∆CAB) = 128 cm².
(ii) area of CAB, if ar (∆CPQ) = 72 cm².

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360. In the given triangle PQR, LM is parallel to QR and PM : MR = 3 : 4. Calculate the value of ratio:
(i)

PL over PQ space and space then space LM over QR comma

(ii)

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