Question

If ΔABC and ΔDEF are two triangles such that AB/DE = BC/EF =CA/FD =2/5, then Area (ΔABC): Area (ΔDEF) =
A. 2 : 5
B. 4 : 25
C. 4 : 15
D. 8 : 125

Answer 1

Answer: B

ΔABC∽ΔDEF is true because of SSS.

And we are given the ratio of similarity. 2:5.

¹*Ratio of area is 2²:5²=4:25.

Answer is B.

¹*Because base and height of two triangles follows the ratio.

Let the ratio of similarity be a:b

Then area of first triangle is (1/2)*base*a*height*a

Second triangle is (1/2)*base*b*height*b

Hence proved. The ratio of area is a²:b².

Answer 2

Answer:

In ΔABC, D and E are points on side AB and AC respectively such that DE||BC and AD: DB = 3 : 1. If EA = 3.3 cm, then AC =

A. 1.1 cm

B. 4 cm

C. 4.4 cm

D. 5.5 cm

Step-by-step explanation: