Question

ΔABC and ΔBDE are two equilateral triangles such that D is the mid-point of BC. The ratio of the areas of triangles ABC and BDE is
A. 2 : 1
B. 1 :2
C. 4 : 1
D. 1 : 4

Answer 1

Step-by-step explanation:

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Answer 2

C. 4 : 1

Step-by-step explanation:

Given:

ΔABC, ΔBDE are equilateral triangles.

BD = BC/2

BC = 4.5 cm.

To find: Ratio of area.

Solution:

Since the triangles are equilateral, the ratio of their sides will be equal.

AB/BE = AC/ED = BC/BD

ΔABC ~ ΔBDE (SSS)

Ratio of area of triangle = ratio of the square of their corresponding sides.

Area of ΔABC / Area of ΔBDE = BC²/BD²

= BC²/(BC/2)²

= 4BC²/BC²

= 4:1

Option C is the answer.