Question

Rectangle A has one side which is 6cm long and the other is (x+2)cm long. Rectangle Y has sides of length (2x+1) and 3cm, If the perimeters are the same, calculate the value of x and hence, the lengths of the sides of the rectangles.

Answer 1

Hello, 

Rectangle A:           6cm                  (x+2)cm
Rectangle B:           3cm                  (2x+1)cm

The formula for the perimeter of a rectangle is: P=2(base+height)

Then:

$P_A=2(b+h) \\ P_A=2*[6+(x+2)] \\ P_A=2*(x+8) \\ P_A=2x+16 \\ \\ \\ P_B=2(b+h) \\ P_B=2*[3+(2x+1)] \\ P_B=2*(2x+4) \\ P_B=4x+8$

But we know that the perimeters are the same, so:

$P_A=P_B \\ 2x+16=4x+8 \\ 8=2x \\ \boxed{x=4} \\ \\ Replacing: \\ \\ Lenght\,\,of\,\,A=(x+2)cm\\ Lenght\,\,of\,\,A=(4+2)cm\\ \boxed{Lenght\,\,of\,\,A=6cm}\\ \\ Lenght\,\,of\,\,B=(2x+1)cm\\ Lenght\,\,of\,\,B=(2*4+1)cm\\ \boxed{Lenght\,\,of\,\,B=9cm}$

With the answer of A, we realize that this figure is actually a square.