Question

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

ac = \frac{c}{3}
bd = 4 - c

Explanation:

Step1: Recall rectangle property

In a rectangle, the diagonals are equal. So $AC = BD$.

Step2: Set up the equation

Set $\frac{c}{3}=4 - c$.

Step3: Solve the equation for c

Multiply both sides by 3 to get $c = 3(4 - c)$. Expand: $c=12 - 3c$. Add $3c$ to both sides: $c + 3c=12$, so $4c = 12$. Divide both sides by 4, we have $c = 3$.

Step4: Find the length of the diagonal

Substitute $c = 3$ into either $AC$ or $BD$ formula. Using $AC=\frac{c}{3}$, we get $AC=\frac{3}{3}=1$. Using $BD = 4 - c$, we get $BD=4 - 3=1$.

Answer:

1