Q6 of 49 Page 25

Δ ABC and ΔDEF are equilateral triangles. If A(ΔABC) : A(ΔDEF) = 1 : 2 and AB = 4, find DE.

We know that, all the angles of an equilateral triangles are equal, i.e., 60°.

⇒ Δ ABC~Δ DEF ……(By AAA Similarity Test)


⇒


And, (Given)


⇒


⇒ DE2 = 2× 42 (∵ AB = 4)


⇒ DE = √32


⇒ DE = 4√2


More from this chapter

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4

ΔLMN ~ ΔPQR, 9 × A(ΔPQR) = 16 × A (ΔLMN). If QR = 20 then find MN.

 5

Areas of two similar triangles are 225 sq.cm & 81 sq.cm. If a side of the smaller triangle is 12 cm, then find corresponding side of the bigger triangle.

 7

In figure 1.66, seg PQ || seg DE, A(Δ PQF) = 20 units, PF = 2 DP, then find A(DPQE) by completing the following activity.

A(Δ PQF) = 20 units, PF = 2 DP, Let us assume DP = x. ∴ PF = 2x



In Δ FDE and Δ FPQ,


∠FDE ≅ ∠ .......... corresponding angles


∠FED ≅ ∠ ......... corresponding angles


∴ Δ FDE ~ Δ FPQ .......... AA test



 1

Select the appropriate alternative.

In Δ ABC and ΔPQR, in a one to one correspondence then