Answer:
AC = BD = 1 unit
Step-by-step explanation:
Given : length of diagonal of rectangle ABCD [tex]AC=\frac{3y}{5}[/tex] and [tex]BD=3y-4[/tex]
We have to find the length of diagonal.
We know In rectangle diagonal are of equal lengths.
Therefore, for rectangle ABCD diagonals AC= BD
Substitute the values, we get,
[tex]\frac{3y}{5}=3y-4[/tex]
Cross multiply , we get
[tex]3y=5(3y-4)[/tex]
On simplyfy , we get
[tex]3y=15y-20[/tex]
Solve for y , we get
[tex]15y-3y=20[/tex]
[tex]12y=20[/tex]
Divide both side by 12, we get,
[tex]y=\frac{20}{12}=\frac{10}{6}[/tex]
Thus, put the values of y in AC and BD to find the length of diagonals , we get,
[tex]AC=\frac{3y}{5}=\frac{3}{5}\times\frac{10}{6}=1[/tex]
Similarly for BC, we get,
[tex]BD=3y-4=3(\frac{10}{6})-4=5-4=1[/tex]
Thus, AC = BD = 1 unit
