Question

what is the perimeter of parallelogram abcd, and what is ac? perimeter = \square ac = \square

Explanation:

Step1: Find perimeter of parallelogram

A parallelogram with perpendicular diagonals is a rhombus, so all sides = 17.
Perimeter = $4 \times 17 = 68$

Step2: Calculate half-length of AC

Use Pythagorean theorem on $\triangle AOB$ (O is diagonal intersection):
Let $AO = x$, then $x^2 + 8^2 = 17^2$
$x^2 = 17^2 - 8^2 = 289 - 64 = 225$
$x = \sqrt{225} = 15$

Step3: Find full length of AC

$AC = 2 \times AO = 2 \times 15 = 30$

Answer:

perimeter = 68
AC = 30