Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

what are the side lengths of a rectangle if the area = 40 in and the perimeter = 48 in

Sagot :

4, 10, 4, 10. 10*4 gives area of 40. 10+10+4+4 gives 48 as shown in question
kate200468
[tex]a,b-the\ side\ lengths\ of\ a\ rectangle\\ \\a\cdot b=40\ [in^2]\ \ \wedge\ \ \ 2\cdot(a+b)=48\ [in]\\ \\ a+b=24\ \ \ \Rightarrow\ \ \ a=24-b\ \ \ \Rightarrow\ \ \ ab=(24-b)b=24b-b^2\\ \\ab=40\ \ \ \Rightarrow\ \ \ 24b-b^2=40\ \ \ \Rightarrow\ \ \ -b^2+24b-40=0\ /\cdot(-1)\\ \\b^2-24b+40=0\ \ \Rightarrow\ \Delta=(-24)^2-4\cdot40=576-160=416=16\cdot 26\\ \\ [/tex]

[tex]\sqrt{\Delta} =4 \sqrt{26} \ \ \ \Rightarrow\ \ \ b_1= \frac{24-4 \sqrt{26} }{2}=12-2 \sqrt{26}\ \Rightarrow\ a_1=12+2 \sqrt{26} \\ \\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ b_2= \frac{24+4 \sqrt{26} }{2}=12+2 \sqrt{26}\ \Rightarrow\ a_2=12-2 \sqrt{26}[/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.