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 given quadrilaterals are similar, then find the value of $x$ and $y$ .

Accepted Answer

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

From the given figure, we observe that $A B ∥ D C$ and $A D ∥ B C$ .

Hence, $A B C D$ is a parallelogram. [If the opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram]

So, $A B = D C = 8$ [The opposite sides of a parallelogram have the same length]

Also, we have, $∠ B C D + ∠ A D C = 180 °$ [The adjacent angles in a parallelogram is supplementary]

$\Rightarrow y ° + ∠ A D C = 180 °$

$\Rightarrow ∠ A D C = 180 ° - y °$ . ----(i)

We know that in two similar quadrilaterals, the corresponding sides are proportional.

Here, $A B C D ~ E F G H$ . So, we have $\frac{A B}{H E} = \frac{B C}{E F} = \frac{C D}{F G} = \frac{A D}{H G}$ . ------(ii)

Now, $\frac{A B}{H E} = \frac{A D}{H G} \Rightarrow \frac{8}{12} = \frac{x + 2}{15}$ [From (ii)]

$\Rightarrow 12 (x + 2) = 8 \times 15$

$\Rightarrow 12 x + 24 = 120$

$\Rightarrow 12 x = 120 - 24$

$\Rightarrow 12 x = 96$

$\Rightarrow x = \frac{96}{12}$

$\Rightarrow x = 8$

Also, we know that in two similar quadrilaterals, the corresponding angles are the same.

Here, in similar quadrilaterals $A B C D$ and $E F G H$ , $∠ A D C$ is the corresponding angle of $∠ F G H$ . So, they are equal.

So, $∠ F G H = ∠ A D C$

$\Rightarrow 70 ° = 180 ° - y °$ [From (i)]

$\Rightarrow y ° = 180 ° - 70 °$

$\Rightarrow y ° = 110 °$

$\Rightarrow y = 110$

Therefore, the required value of $x$ is $8$ and that of $y$ is $110$

If the given quadrilaterals are similar, then find the value of $x$ and $y$ .

Important Questions on Similarity in Geometrical Shapes

Learn and Prepare for any exam you want !

If the given quadrilaterals are similar, then find the value of x and y.

Important Questions on Similarity in Geometrical Shapes

Learn and Prepare for any exam you want !

If the given quadrilaterals are similar, then find the value of $x$ and $y$ .