If ABC- DEF and if A ABC- 9 cm 2- A DEF- 64 cm 2- DE-5-6 cm- then find AB-

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Byju's Answer

Standard X

Mathematics

Relation between Areas and Sides of Similar Triangles

If ABC∼ DEF...

Question

If $△ A B C \sim △ D E F$ and if $A △ A B C = 9 {c m}^{2}$ , $A △ D E F = 64 {c m}^{2}$ , $D E = 5.6 c m$ , then find $A B$ .

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Solution

For similar triangles,
ratio of area of triangles = ratio of square of corresponding sides
Hence, $\frac{A r . △ A B C}{A r . △ D E F} = \frac{A B^{2}}{D E^{2}}$
$\frac{9}{64} = \frac{A B^{2}}{(5.6)^{2}}$
$A B^{2} = \frac{9}{64} (5.6 \times 5.6)$
$A B^{2} = 4.41$
$A B = 2.1 c m$

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Q. ABC

~

DEF

If A (△ ABC) = 9 {cm}^{2}, A (△ DEF) = 64 {cm}^{2} and DE = 5.6 cm, then find AB .

Q. Triangles ABC and DEF are similar.

(i) If area (∆ABC) = 16 cm², area (∆DEF) = 25 cm² and BC = 2.3 cm, find EF.
(ii) If area (∆ABC) = 9 cm², area (∆DEF) = 64 cm² and DE = 5.1 cm , find AB.
(iii) If AC = 19 cm and DF = 8 cm, find the ratio of the area of two triangles.
(iv) If area (∆ABC) = 36 cm², area (∆DEF) = 64 cm² and DE = 6.2 cm, find AB.
(v) If AB = 1.2 cm and DE = 1.4 cm, find the ratio of the areas of ∆ABC and ∆DEF.

Trinagles ABC and DEF are similar.
(i) If area $(Δ A B C) = 16 c m^{2}, a r e a (Δ D E F) = 25 c m^{2}$ and BC = 2.3 cm find EF.
(ii) If area $(Δ A B C) = 9 c m^{2}, a r e a (Δ D E F) = 64 c m^{2}$ and DE=5.1 cm, find AB.
(iii) If AC = 19 cm adn DF = 8 cm, find the ratio of the area of two triangles.
(iv) If area $(Δ A B C) = 36 c m^{2}$ , are $(Δ D E F) = 64 c m^{2}$ and DE= 6.2 cm, find AB.
(v) If AB = 1.2 cm and DE=1.4 cm, find the ratio of the areas of $Δ A B C$ and $Δ D E F$ .