Question

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

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

Explanation:

Step1: Use rectangle property

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

Step2: Solve the equation for y

First, multiply through by 5 to get rid of the fraction: $3y = 5(3y - 4)$. Expand the right - hand side: $3y=15y - 20$. Then, subtract $3y$ from both sides: $0 = 15y-3y - 20$, which simplifies to $0 = 12y - 20$. Add 20 to both sides: $12y=20$. Divide both sides by 12: $y=\frac{20}{12}=\frac{5}{3}$.

Step3: Find the length of the diagonal

Substitute $y = \frac{5}{3}$ into the expression for either diagonal. Using $AC=\frac{3y}{5}$, we have $AC=\frac{3\times\frac{5}{3}}{5}=\frac{5}{5}=1$.

Answer:

1