Ck90idn
Answered

Join IDNLearn.com and become part of a knowledge-sharing community that thrives on curiosity. Get accurate and comprehensive answers to your questions from our community of knowledgeable professionals.

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 :

Illuminati750idn
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 participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. IDNLearn.com is your go-to source for dependable answers. Thank you for visiting, and we hope to assist you again.