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.
[tex]AD=AC[/tex] ...(i)
[tex]3x-5=5y-4[/tex] ...(ii)
In triangle ABD,
[tex]\angle BAD=\angle ABD[/tex]
Base angles are equal, so triangle ABD is an isosceles triangle.
[tex]AD=BD[/tex] ...(iii)
Using (i) and (iii), we get
[tex]AC=BD[/tex]
[tex]5y-4=y+12[/tex]
[tex]5y-y=4+12[/tex]
[tex]4y=16[/tex]
Divide both sides by 4.
[tex]y=4[/tex]
Putting y=4 in (ii), we get
[tex]3x-5=5(4)-4[/tex]
[tex]3x-5=20-4[/tex]
[tex]3x-5=16[/tex]
Adding 5 on both sides, we get
[tex]3x=16+5[/tex]
[tex]3x=21[/tex]
Divide both sides by 3.
[tex]x=7/tex]
Therefore, the value of x is 7 and the value of y is 4.
