Question

1. abcd is a rectangle. find the length of each diagonal. ac = \frac{c}{3} bd = 4 - c 3 4 2 1

Explanation:

Step1: Use property of rectangle diagonals

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

Step2: Solve the equation for c

Multiply both sides of the equation by 3 to get $c = 3(4 - c)$.
Expand the right - hand side: $c=12 - 3c$.
Add $3c$ to both sides: $c + 3c=12$, which simplifies to $4c = 12$.
Divide both sides by 4: $c = 3$.

Step3: Find the length of the diagonal

Substitute $c = 3$ into the expression for either diagonal. Using $AC=\frac{c}{3}$, we have $AC=\frac{3}{3}=1$.
Using $BD = 4 - c$, we have $BD=4 - 3=1$.

Answer:

1