Name: Areas of Similar Triangles
Uploaded: 2019-07-19
Duration: 6 min 54 s
Description: The corresponding sides of similar triangles are proportional. Are the ratios of areas of similar triangles the same as that of their sides? Watch this video...

Question

If the ratio of the perimeters of two regular hexagon is

5 : 4

, then what is the ratio of their sides?

Accepted Answer

We know that, two regular hexagons are always similar.

So, the hexagons $A B C D E F$ and $P Q R S T U$ are similar polygons.

Hence, their corresponding sides will be proportional.

$\Rightarrow \frac{A B}{P Q} = \frac{B C}{Q R} = \frac{C D}{R S} = \frac{D E}{S T} = \frac{E F}{T U} = \frac{A F}{P U} . . . . . (i)$

Also, in regular hexagon, 6 sides are of equal length.

$\Rightarrow A B = B C = C D = D E = E F = F A . . . . (ii)$ and

$P Q = Q R = R S = S T = T U = U P . . . . . (iii)$

Now, it is given that, perimeter of two hexagons are in the ratio $5 : 4$

$\Rightarrow \frac{A B + B C + C D + D E + E F + F A}{P Q + Q R + R S + S T + T U + U P} = \frac{5}{4}$

From $(ii)$ and $(iii)$ , we get

$\frac{A B + A B + A B + A B + A B + A B}{P Q + P Q + P Q + P Q + P Q + P Q} = \frac{5}{4}$

$\Rightarrow \frac{6 A B}{6 P Q} = \frac{5}{4}$

$\Rightarrow \frac{A B}{P Q} = \frac{5}{4}$

From $(i)$ , $\frac{A B}{P Q} = \frac{B C}{Q R} = \frac{C D}{R S} = \frac{D E}{S T} = \frac{E F}{T U} = \frac{A F}{P U} = \frac{5}{4}$

Therefore, ratio of sides of the two regular hexagon is $5 : 4$

If the ratio of the perimeters of two regular hexagon is $5 : 4$ , then what is the ratio of their sides?

Important Questions on Similarity in Geometrical Shapes

Learn and Prepare for any exam you want !

If the ratio of the perimeters of two regular hexagon is 5:4, then what is the ratio of their sides?

Important Questions on Similarity in Geometrical Shapes

Learn and Prepare for any exam you want !

If the ratio of the perimeters of two regular hexagon is $5 : 4$ , then what is the ratio of their sides?