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Standard VIII

Mathematics

Relation between area and sides of similar triangles

If the triang...

Question

If the triangles ABC and DEF are similar, what is the area (in $c m^{2}$ ) of the triangle DEF?

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Solution

Solution:
Apply formula to get the area of triangle ABC as 16 $c m^{2}$ .
Then, apply the rule that the ratio of areas of two similar triangles is equal to the square of the ratio of their sides.

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Similar questions

Q. Triangles

A B C

and

D E F

are similar .The area of

△ A B C

16 c m^{2}

, and that of

△ D E F 25 c m^{2}

. If

B C = 2.3 c m

, find

E F

In given figure $△$ ABC and $△$ DEF are similar, BC = 3cm, EF = 4cm, and area of triangle ABC = 54 $c m^{2}$ . The area of $△$ DEF is ___ ${c m}^{2}$ .

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.

Q. Triangles ABC and DEF are similar.

(i) If area (

△ A B C

)= 16

{cm}^{2}

, area(

△

DEF)= 25

{cm}^{2}

and

B C = 2.3 cm

, find

E F

(ii) If area (

△ A B C

)= 9

{cm}^{2}

, area(

△

DEF) = 64

{cm}^{2}

and

D E = 5.1 cm

, find

A B

(iii) If

A C = 19 cm

and

D F = 8 cm

, find ratio of the area of two triangles.

(iv) If area (

△ A B C

)= 36

{cm}^{2}

, area (

△

DEF) =64

{cm}^{2}

and

D E = 6.2 cm

, find

A B

(v) If

A B = 1.2 cm

and

D E = 1.4 cm

, find the ratio of the areas of triangle

A B C

and

D E F

Q. Triangles ABC and DEF are similar. If their areas are 64

c m^{2}

and 49

c m^{2}

and if AB is 7 cm, then find the value of DE.

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If the triangles ABC and DEF are similar, what is the area (in cm2) of the triangle DEF?

Solution: Apply formula to get the area of triangle ABC as 16 cm2. Then, apply the rule that the ratio of areas of two similar triangles is equal to the square of the ratio of their sides.

If the triangles ABC and DEF are similar, what is the area (in $c m^{2}$ ) of the triangle DEF?

Solution:
Apply formula to get the area of triangle ABC as 16 $c m^{2}$ .
Then, apply the rule that the ratio of areas of two similar triangles is equal to the square of the ratio of their sides.