Question

ANGLE ABC IS SIMILAR TO ANGLE DEF AND THEIR AREAS ARE 64CM2 AND 100CM2 RESPECTIVELY .IF EF=12CM THEN FIND THE MEASURE OF BC​

Answer 1

Answer:

The measure of bc is 9.6 cm

Theorem : The ratio of the area of two similar triangles is equal to the ratio of the squares of their corresponding sides .

We are given that ∆ abc ~ ∆ def and their areas are 64cm2 and 100cm2 respectively and ef=12cm

So,\frac{(bc)^2}{(ef)^2}=\frac{64}{100}

(ef)

2

(bc)

2

=

100

64

\frac{(bc)^2}{(12)^2}=\frac{64}{100}

(12)

2

(bc)

2

=

100

64

(bc)^2=\frac{64}{100} \times 12^2(bc)

2

=

100

64

×12

2

(bc)^2=92.16(bc)

2

=92.16

bc = \sqrt{92.16}bc=

92.16

bc=9.6 cm

Hence the measure of bc is 9.6 cm