Rectangle call a special case of a quadrangle - the closed geometrical figure made of four pieces which are not lying on one straight line in pairs connecting four tops of this polygon. Distinctive feature of a rectangle are corners in 90 °, lying in each its top. This feature considerably simplifies a problem of finding of length of diagonal of a figure, almost always reducing it to Pythagorean theorem.
Instruction
1. Use Pythagorean theorem for calculation of length of diagonal (D) rectangle if from statements of the problem width (W) and height (H) of a figure are known. The diagonal and two parties of this quadrangle forming a right angle opposite to it create a rectangular triangle, and Pythagorean theorem says that the hypotenuse length square is equal in such triangle to the sum of squares of lengths of its legs. In this case a hypotenuse is diagonal, and it means that for finding of its length you should find a root from the sum squared lengths and width of a rectangle: D= √ (W²+H²).
2. Modify the received formula if length only of one party of a rectangle (for example, H) is known and its (S) Square. The missing party in the formula received on the previous step can be replaced with a ratio between the area and length of the known party. Substitute this ratio in a formula: D= √ (H²+(S/H)²)= √ (H²+S²) / H.
3. In the similar way change a formula from the first step if length of one party (H) and length of perimeter (P) of a rectangle are known. The perimeter is made on two lengths of each of the parties of a figure, and it means that instead of length of the unknown party a formula it is possible to substitute expression (P-2*H)/2 or P/2-H: D= √ (H²+(P/2-H)²= √ (H²+P²/4-P*H+H²)= √ (2*H²+P²/4-P*H).
4. If it is possible to enter a circle in a rectangle, then this rectangle is a square, so, length of any its party is equal to diameter of this circle (d). Substitute this value in a formula from the first step: D= √ (d²+d²) =d * √ 2.
5. It is possible to do without Pythagorean theorem in case diameter of the circle described about a rectangle is known. It is the simplest option of finding of diagonal of a rectangle - length of diagonal coincides with diameter of a circle.