- ABC - DEF such that ar - ABC - 64 cm2 and ar - DEF - 169 cm2- If BC - 4 cm- find EF-

Since triangle ABC is similar to triangle DEF. Therefore(Area ABC)/ (Area DEF) =BC^2/EF^2 Because the ratio of area of two similar triangles is equal to the r ...

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Standard X

Mathematics

Relation between Areas and Sides of Similar Triangles

Δ ABC ∼Δ DEF ...

Question

$Δ A B C \sim Δ D E F$ such that ar $(Δ A B C)$ = 64 $c m^{2}$ and ar $(Δ D E F) = 169 c m^{2}$ . If BC = 4 cm, find EF.

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Solution

Since triangle ABC is similar to triangle DEF.

Therefore $\frac{(A r e a △ A B C)}{(A r e a △ D E F)} = \frac{{B C}^{2}}{{E F}^{2}}$

Because the ratio of area of two similar triangles is equal to the ratio of square of their corresponding sides.

$\frac{64}{169} = \frac{4^{2}}{E F}$

$6 * \frac{169}{64}$

EF = 42.25 cm

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ΔABC∼ΔDEF such that ar (ΔABC) = 64 cm2 and ar (ΔDEF)=169cm2. If BC = 4 cm, find EF.

Since triangle ABC is similar to triangle DEF. Therefore(Area△ABC)(Area△DEF)=BC2EF2 Because the ratio of area of two similar triangles is equal to the ratio of square of their corresponding sides. 64169=42EF 6∗16964 EF = 42.25 cm

$Δ A B C \sim Δ D E F$ such that ar $(Δ A B C)$ = 64 $c m^{2}$ and ar $(Δ D E F) = 169 c m^{2}$ . If BC = 4 cm, find EF.