Question

if in the 1 figure triangle are similar and in figure-2 quadrilateral are similar then find the value of x and y​

Answer 1

Answer:

dont know!!! which class,s it is

Answer 2

1)Since, the given triangle are similar, hence their corresponding sides will be proportional.

∴ As given in the figure,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{10}{6} = \frac{15}{x - 2}$

$⟹\: \: \: \: \: \: \: \: \: \: \: \frac{5}{3} = \frac{15}{x - 2}$

$⟹ \: \: \: \: \: \: \: \: \: \: \: \: \: \: 5x - 10 = 45$

$⟹ \: \: \: \: \: \: \: \: \: \: \: \: \: 5x = 45 + 10 = 55$

$∴ \: \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{55}{5} = 11$

$and \: \: \: \: \: \: \: \: \frac{8}{10} = \frac{y + 3}{15}$

$⟹ \: \: \: \: \: \frac{4}{5} = \frac{y + 3}{15}$

$⟹ \: \: \: \: \: \: \: \: \: 5y + 15 = 60$

$⟹ \: \: \: \: \: \: \: \: \: \: 5y = 60 - 15 = 45$

$∴ \: \: \: \: \: \: \: \: \: \: \: y = \frac{45}{5} = 9$

Hence, x = 11, y = 9.

2)since, the given quadrilateral are similar, hence their corresponding sides are proportion.

$∴ \: \: \: \: \: \: \: \: \: \: \frac{x + 2}{8} = \frac{15}{12}$

[ ∵ given quadrilaterals are parallelogram, hence in the large quadrilateral the side opposite to 12 will also 12]

$⟹ \: \: \: \: \: \: \: \: \: \: \: \frac{x + 2}{8} = \frac{5}{4}$

$⟹ \: \: \: \: \: \: \: 4x + 8 = 40$

$⟹ \: \: \: \: \: \: \: \: \: 4x = 40 - 8 = 32$

$∴ \: \: \: \: \: \: \: \: x = \frac{32}{4} = 8.$

Since, corresponding angles in similar quadrilateral are equal, hence the corresponding angles of 70° in the large quadrilateral is also 70° in the small quadrilateral. Now, since, the quadrilaterals are parallelogram, hence the angle 70° and the angle of y°are the interior angles of the same side. Hence their sum will be 180°.

$∴ \: \: \: \: \: \: \: \: y + 70° = 180°$

$⟹ \: \: \: \: \: \: \: \: \: y = 180° - 70° = 110°$

Thus, x = 8, y = 110°.