A Rectangle Is Inscribed In An Equilateral Triangle Of Side Length 2 A Units The Maximum Area Of
A Rectangle Is Inscribed In An Equilateral Triangle Of Side Lengthо A = (25sqrt(3)) 2 first, let's look at a picture. some initial observations: the area a of the rectangle is a=bh. by symmetry, the base of the triangle is of length b 2t, and thus, as it is of length 10, we have b 2t = 10 => t = 5 b 2 if we decide b that also determines h, and thus we can write h as a function of b. to write h as a function of b, we can look at the right triangle with legs t. If the ellipse x 2 a 2 y 2 b 2 = 1 is inscribed in a rectangle whose length to breadth ratio is 2: 1 in such a manner that it touches the sides of rectangle, then the area of the rectangle is q. if a circle is inscribed in an equilateral triangle of side a, then area of the square inscribed in the circle is.
If A Rectangle Is Inscribed In An Equilateral Triangle Of Side Leng The maximum area of this rectangle can be(a) \( \sqrt{3} a^{2} \)(b) \( \ a rectangle is inscribed in an equilateral triangle of side length \( 2 a \) units. Hint: proceeding the question by first drawing the figure, we try to evaluate the area of the rectangle inscribed in the equilateral triangle in terms of only one variable. then we will differentiate the obtained area to get the value of the variable at which the area is maximum. complete step by step answer:. My applications of derivatives course: kristakingmath applications of derivatives courselearn how to find the dimensions of the rectangle t. A rectangle is inscribed in an equilateral triangle, with one side on a side of the triangle. if the triangle has side of length 2, what is the maximum possible area of the rectangle?.
![Dimensions Of rectangle With maximum area inscribed In equilateral Dimensions Of rectangle With maximum area inscribed In equilateral](https://ytimg.googleusercontent.com/vi/ucLv2iAt71U/maxresdefault.jpg)
Dimensions Of Rectangle With Maximum Area Inscribed In Equilateral My applications of derivatives course: kristakingmath applications of derivatives courselearn how to find the dimensions of the rectangle t. A rectangle is inscribed in an equilateral triangle, with one side on a side of the triangle. if the triangle has side of length 2, what is the maximum possible area of the rectangle?. The maximum area is 25sqrt(3) 2 this'll be quite a long answer, hopefully it makes sense, but sorry about the length. let's call the length, or the side that is on the base of the triangle, l. l can be any number between 0 and 10, as it fits the base of the triangle exactly. the width is the hard part, as it is the part from the base of the triangle to one of the sides of the triangle. first. Solution 1 (coordinate bash) consider points on the complex plane . since the rectangle is quite close to a square, we figure that the area of the equilateral triangle is maximized when a vertex of the triangle coincides with that of the rectangle. set one vertex of the triangle at , and the other two points and on and , respectively.
![a Rectangle is Inscribed in An Equilateral triangle of Side lengthо a Rectangle is Inscribed in An Equilateral triangle of Side lengthо](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1471482/original_1402.png)
A Rectangle Is Inscribed In An Equilateral Triangle Of Side Lengthо The maximum area is 25sqrt(3) 2 this'll be quite a long answer, hopefully it makes sense, but sorry about the length. let's call the length, or the side that is on the base of the triangle, l. l can be any number between 0 and 10, as it fits the base of the triangle exactly. the width is the hard part, as it is the part from the base of the triangle to one of the sides of the triangle. first. Solution 1 (coordinate bash) consider points on the complex plane . since the rectangle is quite close to a square, we figure that the area of the equilateral triangle is maximized when a vertex of the triangle coincides with that of the rectangle. set one vertex of the triangle at , and the other two points and on and , respectively.
![a Rectangle is Inscribed in An Equilateral triangle So That One side O a Rectangle is Inscribed in An Equilateral triangle So That One side O](https://useruploads.socratic.org/cT5XWxgZTOmG9veOhtec_triangle.png)
A Rectangle Is Inscribed In An Equilateral Triangle So That One Side O
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