MATH SOLVE

4 months ago

Q:
# On a coordinate plane, parallelogram P Q R S is shown. Point P is at (negative 2, 5), point Q is at (2, 1), point R is at (1, negative 2), and point S is at (negative 3, 2). In the diagram, SR = 4 StartRoot 2 EndRoot and QR = StartRoot 10 EndRoot. What is the perimeter of parallelogram PQRS? StartRoot 10 EndRoot units 8 StartRoot 2 EndRoot + 2 StartRoot 10 EndRoot units 16 StartRoot 2 EndRoot units 8 StartRoot 2 EndRoot + 8 units

Accepted Solution

A:

Answer:The perimeter of parallelogram PQRS = [tex]2\sqrt{10}+8\sqrt{2}[/tex] ⇒ 2nd answerStep-by-step explanation:* Lets revise some properties of the parallelogram- Each two opposite sides are parallel- Each two opposite sides are equal- Its perimeter is the twice the sum of two adjacent sides* Lets solve the problem∵ PQRS is a parallelogram∵ The length of side SR is [tex]4\sqrt{2}[/tex]∵ The length of side QR is [tex]\sqrt{10}[/tex]∵ SR and RQ are two adjacent sides∵ The perimeter of parallelogram PQRS = 2(RQ + SR)∴ The perimeter of parallelogram PQRS = [tex]2(\sqrt{10}+4\sqrt{2})[/tex]∵ [tex]2*\sqrt{10}[/tex] = [tex]2\sqrt{10}[/tex]∵ [tex]2*4\sqrt{2}[/tex] = [tex]8\sqrt{2}[/tex]∴ The perimeter of parallelogram PQRS = [tex]2\sqrt{10}+8\sqrt{2}[/tex]