Question

abcd is a rectangle. find the length of each diagonal.
ac = 3(x - 3) and bd = x + 13
ac = \square, bd = \square

Explanation:

Step1: Set diagonals equal

In a rectangle, diagonals are equal: $3(x - 3) = x + 13$

Step2: Solve for x

Expand left side: $3x - 9 = x + 13$
Subtract x: $2x - 9 = 13$
Add 9: $2x = 22$
Divide by 2: $x = 11$

Step3: Calculate AC

$AC = 3(11 - 3) = 3×8 = 24$

Step4: Calculate BD

$BD = 11 + 13 = 24$

Answer:

AC = 24, BD = 24