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