ck90
Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

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.

Sagot :

Illuminati750
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:

[tex]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 [/tex]

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

[tex]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}[/tex]

With the answer of A, we realize that this figure is actually a square.
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.