Question

Find the values of X and Y. ​

Answer 1

Given:

A figure.

To find:

The value of x and y.

Solution:

In triangle ADC, all angles are equal, so it is an equilateral triangle.

We know that, all sides of an equilateral triangle are equal.

`AD=AC` ...(i)

`3x-5=5y-4` ...(ii)

In triangle ABD,

`\angle BAD=\angle ABD`

Base angles are equal, so triangle ABD is an isosceles triangle.

`AD=BD` ...(iii)

Using (i) and (iii), we get

`AC=BD`

`5y-4=y+12`

`5y-y=4+12`

`4y=16`

Divide both sides by 4.

`y=4`

Putting y=4 in (ii), we get

`3x-5=5(4)-4`

`3x-5=20-4`

`3x-5=16`

Adding 5 on both sides, we get

`3x=16+5`

`3x=21`

Divide both sides by 3.

[tex]x=7/tex]

Therefore, the value of x is 7 and the value of y is 4.