Question

triangle AbC is similar to DEF. Area of ABC and DEF is 9 cm2 and 16 cm2 respectively. BC = 2.1 cm. What will be the length of EF

Answer 1

Hope this help......

Answer 2

Answer:

The length of side EF is 2.8cm

Step-by-step explanation:

Given that the triangles ∆ABC and ∆DEF are similar triangles.Therefore the ratio of their side are equal.Hence,

$\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}$

We also have another property of similar triangles which states that the ratio of Areas of similar triangles is equal to the ratio of square of their sides.

$\frac{ar(∆ABC)}{ar(∆DEF)}=(\frac{BC}{EF})^{2}$

Substituting the given areas and given side BC ,we get

$\frac{9}{16} = \frac{2.1 {}^{2} }{EF {}^{2} } \\ = > \frac{3}{4} = \frac{2.1}{EF} = > EF = \frac{4}{3} \times 2.1 \\ = 2.8 \: cm$

Therefore,the length of side EF is 2.8cm

#SPJ3