What is the area of the largest equilateral triangle which fits inside a square of side a?

What is the area of the largest equilateral triangle which fits inside a square of side a?

I need help pls! I have a diagram which shows an equilateral triangle ABC, a square APRC and a right angles triangle CRS with CSR=90 degrees. If B,C and S all lie on the same straight line,...

What im ask is like is their some special name for when a number lets say 5 is put so it is like squaring but has a +1 in the second part so 5 = 5 * 6 or 9 = 9 * 10 finally like 29 = 29 * 30 im...

The area of two square is 468m^2 and the difference between their perimeter is 24m . Find the sides of square

Tom was asked to form a square with 56 pots of flowers placed at equal intervals between each other. How many pots of flowers should he place on any one side of the square?

If 3 triangles is equal to 5 disks, and if 1 triangle is equal to 2 squares plus 1 disk, how many squares would it take to balance one disk?

if y is 25 and x is 3 squared. what is y, if x is 2 squared

Mr Smith, the Mathematics teacher for Standard VI, is an exasperated person. He wants to device a way to keep his class of excited students quiet, so he can catch a bit of sleep (he went to late night...

x^2-8x=-13

1. The area of a square is 3 square inches bigger than the area of a rectangle. The width of the rectangle is 3 inches shorter than one side of the square, and the length of the rectangle is 4 inches...

Points E and F are chosen on sides BC and AB respectively of the square ABCD so that the lines DE and DF divide the square into three regions of equal area. The sides of the square have length...

Please help me, I cannot do this no matter what. Also, the other question is what percent of the square's area is the area of the new rectangle..... IF you can pls provide both answers with a explanation...

A square mirror has sides measuring 2 feet less than the sides of a square painting. If the difference between their areas is 32 square feet, find the lengths of the sides of the mirror and painting...

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A quadrilateral has diagonals that do NOT bisect each other. Which of the following types of quadrilaterals could it be? A)Parallelogram B) Rectangle C) Rhombus D)...

A). 2n^2=-10n-6 B). z^2-14z+34=0

The answer choices are: √128, 3√128, 128^2, 128^3

Find all 2x2 matrices A that are symmetric and whose squares are equal to themselves

Two congruent chords AB and CD which are not diameters, intersect at right angle in P. O is the centre of the circle. If M and N are the mid-points of AB and CD respectively, then prove that quadrilateral...

(4√3+√5)(√3-9√5) =