Question

1. abcd is a rectangle. find the length of each diagonal.

ac = \frac{7y}{5}
bd = 3y - 4
-1
\frac{5}{5}
2
1

Explanation:

Step1: Recall property of rectangle diagonals

In a rectangle, the diagonals are equal. So, $AC = BD$. Given $AC=\frac{7y}{5}$ and $BD = 3y - 4$, we set up the equation $\frac{7y}{5}=3y - 4$.

Step2: Solve the equation for y

Multiply through by 5 to get rid of the fraction: $7y=5(3y - 4)$. Expand the right - hand side: $7y = 15y-20$. Subtract $7y$ from both sides: $0=15y - 7y-20$, which simplifies to $0 = 8y-20$. Add 20 to both sides: $20 = 8y$. Then $y=\frac{20}{8}=\frac{5}{2}$.

Step3: Find the length of the diagonal

Substitute $y = \frac{5}{2}$ into the expression for either $AC$ or $BD$. Using $AC=\frac{7y}{5}$, we have $AC=\frac{7\times\frac{5}{2}}{5}=\frac{7}{2}= 3.5$. Using $BD = 3y - 4$, we have $BD=3\times\frac{5}{2}-4=\frac{15}{2}-4=\frac{15 - 8}{2}=\frac{7}{2}=3.5$.

Answer:

None of the provided options (-1, $\frac{5}{5} = 1$, 2, 1) are correct. The length of each diagonal is $\frac{7}{2}$ or 3.5.