Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Answer:
Step-by-step explanation:
That will be a square with a diagonal of 20
side length of 20sin45
and area of (20sin45)² = 200 units²
prove it you say?
Area of a rectangle is base times height
A = bh
With a radius of 10, the diagonals of any rectangle inscribed will be 20 units
20² = b² + h²
h = [tex]\sqrt{400 - b^2}[/tex]
A = bh
A = b[tex]\sqrt{400 - b^2}[/tex]
Area will be maximized when the derivative is set to zero
dA/db = [tex]\sqrt{400 - b^2}[/tex] - b²/ [tex]\sqrt{400 - b^2}[/tex]
0 = [tex]\sqrt{400 - b^2}[/tex] - b²/ [tex]\sqrt{400 - b^2}[/tex]
b²/[tex]\sqrt{400 - b^2}[/tex] = [tex]\sqrt{400 - b^2}[/tex]
b² = 400 - b²
2b² = 400
b² = 200
b = [tex]\sqrt{200}[/tex]
h = [tex]\sqrt{400 - b^2}[/tex]
h = [tex]\sqrt{400 - \sqrt{200}^2 }[/tex]
h = [tex]\sqrt{200}[/tex]
A = bh
A = [tex]\sqrt{200}[/tex]•[tex]\sqrt{200}[/tex]
A = 200 units²
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
