Question

ΔABC ~ ΔDEF, ar (ΔABC ) = 9 cm², ar (ΔDEF) = 16 cm². If BC = 2.1 cm, then the measure of EF is
A. 2.8 cm
B. 4.2 cm
C. 2.5 cm
D. 4.1 cm

Answer 1

Answer:

answer is A......2.8cm

Answer 2

A. 2.8 cm

Step-by-step explanation:

Given:

ΔABC ~ ΔDEF

area of ΔABC  = 9 cm²

area of ΔDEF = 16 cm².

BC = 2.1 cm

To find: EF

For congruent triangles, the ratio of their areas will be in the ratio of the square of their corresponding sides.

So area of ΔABC /  area of ΔDEF = BC² / EF²

9 / 16 = 2.1² / EF²

EF² = 2.1 * 2.1 * 16 / 9

Therefore EF = root of (2.1 * 2.1 * 16 / 9)

 = 2.1 * 4 / 3

 = 0.7 * 4

 = 2.8 cm

Option A is the answer.