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in Triangles by (65.5k points)

In a squared sheet, draw two triangles of equal areas such that

(i) The triangles are congruent.

(ii) the triangles are not congruent. What can you say about their perimeters?

1 Answer

+1 vote
by (65.2k points)
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Best answer

Consider the ∆ PQS and SQR

In ∆ PQS and ∆ SQR

PS = QR = 6 cms

∠SPQ = ∠QRS = 90°

QS = QS = common

By RHS congruence criterion

∆PQS ≅ ∆SQR.

Perimeter of the ∆ PQS = PQ + QS + PS

Perimeter of the ∆ SQR = SR + QS + QR

∴ Perimeter of the ∆ PQS = Perimeter of the ∆

SQR (∵ PQ = SR & PS = QR)

∴ area of ∆ PQS = Area of ∆ PQM.

By seeing the figure the ∆ PQS = PQ + PS + SQ = 8 + 6 + 10 = 24 cms.

Perimeter of the ∆ PQM = PQ + PM + QM

= 8 + 7.2 + 7.2

= 22.4 cms.

∴ Their perimeters are not equal.

PM = QM

(PM)2 = PN2 + MN2

= 42 + 62

= 16 + 36 = 52

PM = QM = \(\sqrt{52}\) = 7.2

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