The equations of the other two sides of the square are The equations of the other two sides of the square â¦ As given, diagonal is equal to 6cm. ... All four sides of a square are equal. The equation of two sides of a square whose area is 2 5 square units are 3 x â 4 y = 0 and 4 x + 3 y = 0. All sides are equal in length, and these sides intersect at 90°. Example 1: Find the sides and area of a square when diagonal is given as 6cm. A square and an equilateral triangle have equal perimeter. Finding the side lengths of a square given diagonalsPhillips Exeter Math 2 @ Foothill HSDan Tating Opposite sides of a square are both parallel and equal in length. Here, âdâ is the length of any of the diagonal (in a square, diagonals are equal) Derivation for Area of Square using Diagonal Formula. The diagonals of a square are equal. Sometimes, however, you might be asked to find the length of the diagonal given another value, such as the perimeter or area of the square. So in a square all of these are true. This means, that dissecting a square across the diagonal will also have specific implications. According to Pythagoras theorem, x 2 + x 2 = 6 2. The Diagonal is the side length times the square root of 2: Diagonal "d" = a × â2. A square is a four-sided shape with very particular properties. And in a diamond, the diagonals are perpendicular to each other. Prove that the diagonals of a square are equal and perpendicular to each other The diagonal of a square is the line stretching from one corner of the square to the opposite corner. To Find : The area of triangle . Let The side of equilateral triangle = s cm. This, it has four equal sides, and four equal vertices (90°). In a rectangle, the diagonals are equal and bisect each other. If the square is divided into two right-angled triangles then the hypotenuse of each triangle is equal to the diagonal of the square. Their hypotenuse is the diagonal of the square, so we can solve for the hypotenuse. The two legs have lengths of 8. Diagonal Length = a × â2 EXPLANATION: The diagonals of a square bisect its angles. Let The side of square = S cm. Let the diagonals AC and BD intersect each other at a point O. Solution: Let us take a square of side x. The diagonal of the square is 12 cm. To prove that the diagonals of a square are equal and bisect each other at right angles, we have to prove AC = BD, OA = OC, OB = OD, and AOB = 90º. We need to use the Pythagorean Theorem: , where a and b are the legs and c is the hypotenuse. square and an equilateral triangle have equal perimeter âµ The perimeter of square = 4 × side To find the diagonal of a square, you can use the formula =, where equals one side length of the square. The diagonal line cuts the square into two equal triangles. Solution : According to question. The diagonals are equal to each other, they bisect each other, and they are perpendicular to â¦ Consider a square of sides âaâ units and diagonal as âdâ units. 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