Question

What is the perimeter of rectangle ABCDABCD? (1) The longer side of the rectangle is 2 meters shorter than its diagonal (2) The ratio of the shorter side of the rectangle to its diagonal is 13

Answer 1

Answer:

(1) P=4a+4

(2) P=2a+4$\sqrt{42}$a

Step-by-step explanation:

Well, let us call longer side b, shorter side a and diagonal d. The perimeter of a rectangle is 2*(a+b). Let us write this formula as P=2*(a+b)

In (1) it is stated that b=a+2. Hence, the perimeter of the rectangle is P=2*(a+b). In terms of b, let us write (a+2). So P=2*(a+a+2)=4a+4.

In (2) it is stated that d/a=13 or d=13a. From Pythagorean theorem d^2=a^2+b^2. Hence, b^2=168a^2 or b=2$\sqrt{42}$a. Finally, P=2*(a+b)=2*(a+2$\sqrt{42}$a)=2a+4$\sqrt{42}$a