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 in the given pair of polygons are similar, then find the value of $x, y$ and $z$ .

Accepted Answer

Given that the two quadrilaterals are similar. We have to find the value of $x, y$ and $z$ .

In the two given quadrilaterals $A B C D$ and $E F G H$ , we observe that $∠ A B C = ∠ E F G, ∠ B A D = ∠ F E H$ and $∠ A D C = ∠ E H G$ .

Hence, the fourth angle $∠ B C D$ will be equal to $∠ F G H$ .

We know that in two similar quadrilaterals the sides opposite to the equal angles are proportional.

Thus, in the given quadrilaterals $A B C D$ and $E F G H$ , we get, $A B$ is proportional to $E F$ , $B C$ is proportional to $F G$ , $C D$ is proportional to $G H$ and $A D$ is proportional to $E H$ .

So, we can write, $\frac{A B}{E F} = \frac{B C}{F G} = \frac{C D}{G H} = \frac{A D}{E H}$ -----(i)

Now, from (i), we get, $\frac{B C}{F G} = \frac{C D}{G H}$

$\Rightarrow \frac{10}{8} = \frac{x}{13}$

$\Rightarrow 8 x = 10 \times 13 = 130$

$\Rightarrow x = \frac{130}{8} = \frac{65}{4} = 16.25$

$\Rightarrow x = 16.25$ .

Again, from (i), we get, $\frac{A B}{E F} = \frac{B C}{F G}$

$\Rightarrow \frac{16}{y} = \frac{10}{8}$

$\Rightarrow 10 y = 16 \times 8 = 128$

$\Rightarrow y = \frac{128}{10} = \frac{64}{5} = 12.8$

$\Rightarrow y = 12.8$

Also, from (i), we get, $\frac{B C}{F G} = \frac{A D}{E H}$

$\Rightarrow \frac{10}{8} = \frac{14}{z}$

$\Rightarrow 10 z = 8 \times 14 = 112$

$\Rightarrow z = \frac{112}{10} = 11.2$

$\Rightarrow z = 11.2$

Therefore, the required value of $x$ is $16.25$ , $y$ is $12.8$ and $z$ is $11.2$

If in the given pair of polygons are similar, then find the value of $x, y$ and $z$ .

Important Questions on Similarity in Geometrical Shapes

Learn and Prepare for any exam you want !

If in the given pair of polygons are similar, then find the value of x, y and z.

Important Questions on Similarity in Geometrical Shapes

Learn and Prepare for any exam you want !

If in the given pair of polygons are similar, then find the value of $x, y$ and $z$ .