Question

in the diagram, sr = 4√2 and qr = √10. what is the perimeter of parallelogram pqrs?
○ √10 units
○ 8√2 + 2√10 units
○ 16√2 units
○ 8√2 + 8 units
(diagram shows a grid with points p(-2,5), s(-3,2), q(2,1), r(1,-2) forming a parallelogram)

Explanation:

Step1: Recall perimeter formula for parallelogram

In a parallelogram, opposite sides are equal. So perimeter \( P = 2\times(\text{length of one pair of sides}+\text{length of the other pair of sides}) \).

Step2: Identify side lengths from given info

We know \( SR = 4\sqrt{2} \) and \( QR=\sqrt{10} \). In parallelogram \( PQRS \), \( PQ = SR \) and \( PS = QR \) (opposite sides of parallelogram are equal).

Step3: Calculate perimeter

Using the perimeter formula: \( P = 2(SR + QR) \). Substitute \( SR = 4\sqrt{2} \) and \( QR=\sqrt{10} \) into the formula.
\( P=2(4\sqrt{2}+\sqrt{10}) = 8\sqrt{2}+2\sqrt{10} \)

Answer:

\( 8\sqrt{2} + 2\sqrt{10} \) units