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Relation between Areas and Sides of Similar Triangles

In the adjoin...

Question

In the adjoining figure, D, E and F are mid-points of the sides BC, CA and AB of triangle ABC. If AB = 4.3cm, BC = 5.6cm and AC = 3.5cm, find the perimeter of triangle
Section B

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Solution

$G i v e n : D, E a n d F a r e t h e m i d p o i n t s o f t h e s i d e s B C, A C a n d A B o f t r i a n g l e A B C . A B = 4.3 c m; B C = 5.6 c m a n d A C = 3.5 c m T o f i n d : P e r i m e t e r o f T r i a n g l e D E F P e r i m e t e r o f D E F = D E + E F + D F U \sin g M i d p o i n t t h e o r e m t h a t i s t h e l i n e j o i n i n g t h e m i d p o i n t s o f t h e t w o s i d e s o f t r i a n g l e i s p a r a l l e l t o t h e t h i r d s i d e a n d e q u a l t o h a l f o f i t .$
$D E = \frac{1}{2} (A B) = \frac{1}{2} \times 4.3 = 2.15 c m E F = \frac{1}{2} (B C) = \frac{1}{2} \times 5.6 = 2.8 c m F D = \frac{1}{2} (A C) = \frac{1}{2} \times 3.5 = 1.75 c m S o, t h e p e r i m e t e r o f D E F = 2.15 + 2.8 + 1.75 = 6.7 c m$

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Similar questions

Q. In figure,

D, E

and

F

are the mid-points of the sides

B C, C A

and

A B

respectively. If

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A C = 3.9 c m

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(i)

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and
(ii) quad.

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Q. In

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In a triangle, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30cm, find the perimeter of the quadrilateral ARPQ.

Q. In the given figure, M, N, and P are the mid-points of AB, AC, and BC, respectively. If MN = 3 cm, NP = 3.5 cm, and MP = 2.5 cm, find the perimeter of the triangle ABC (in cm).

Q. In triangle

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In the adjoining figure, D, E and F are mid-points of the sides BC, CA and AB of triangle ABC. If AB = 4.3cm, BC = 5.6cm and AC = 3.5cm, find the perimeter of triangleSection B

In the adjoining figure, D, E and F are mid-points of the sides BC, CA and AB of triangle ABC. If AB = 4.3cm, BC = 5.6cm and AC = 3.5cm, find the perimeter of triangle
Section B