anonymous
  • anonymous
Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side L=2 cm if one side of the rectangle lies on the base of the triangle.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
dumbcow
  • dumbcow
max Area = sqrt(3)/2
anonymous
  • anonymous
On the side of the triangle shared with a side of the rectangle call x the distance from one corner of the triangle to the start of the base of the rectangle. Then the height of the rectangle is x*tan(60)=x*sqrt(3). So the area is (2-2x)*(x*sqrt(3))=2xsqrt(3)-2x^2sqrt(3). We take the derivative and set equal to 0. 2sqrt(3)-4sqrt(3)x=0 x=1/2 So the base is 1 and the height is sqrt(3)/2 Max area =sqrt(3)/2
anonymous
  • anonymous
Thank you both very much!

Looking for something else?

Not the answer you are looking for? Search for more explanations.