A rectangle is inscribed in a semicircle of radius 10 cm. What is the area of the largest rectangle we can inscribe? A = xw (w 2)2 ... A = 2x (100 x2)1=2 dA dx = 2x 1 ... A semicircle has symmetry, so the center is exactly at the midpoint of the 2 side on the rectangle, making the radius, by the Pythagorean Theorem, . The area is . Solution 2. Double the figure to get a square with side length . The circle inscribed around the square has a diameter equal to the diagonal of this square. The diagonal of this ...

2nd, a semicircle divides into 2 equal quarter circles; when doing so equal isosceles right triangles are formed. In a 45–45–90 triangle if the hypotenuse ( radius of the circle) = 2, each leg = square root of 2.Thus the length of inscribed rectangle is 2(square root of 2) and the width is square root of two. area of rectangle is l(w) 2/8/2010 · 1 Find the dimensions of the largest rectangle that can be inscribed in a triangle whose base is 8 and altitude 12. Express the area in terms of h. {Hint: Use Similar Triangles} 2 A line segment 20 units long is divided into two segments 4x and (20−4x), with 4x becoming the circumference of a circle and 20−4x, the perimeter of a square.

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