Rectangle - one of the simplest geometrical figures which, having all corners identical and equal 90 °, is a special case of a parallelogram. The piece connecting two tops of a rectangle which do not have the general party is called the diagonal of this polygon. It is possible to calculate diagonal length in several ways depending on the known basic data.
Instruction
1. If lengths of both parties are known (A and B) a rectangle, length of diagonal (C) it is possible to define as a square root from the sum of squares of lengths of the parties. It follows from Pythagorean theorem as diagonal in this geometrical figure forms a rectangular triangle which two other parties are the parties of a rectangle. Diagonal in this triangle is a hypotenuse, and the parties of a rectangle - legs. That is: C= √ (A²+B²).
2. If length of one of the parties is unknown, but length of other (A) and the area (S) of a rectangle is known, then diagonal length can be calculated too. As the area of a rectangle is multiplication of lengths of its parties, the unknown party can be expressed as private from division of the square at length of other party. Substitute this expression in the formula received on the first step: C= √ (A²+S²/A²)= √ (A +S²) / A.
3. If length of one of the parties of a rectangle (A) and also length of its perimeter (P) is known, then length of the second party can be determined too. As the perimeter in a rectangle is the doubled sum of two parties, each party can be defined as a difference between poluperimetry and length of other party. Substitute this expression in the same formula from the first step: C= √ (A²+(P/2-A)²= √ (A²+P²/4-P×A+A²)= √ (2×A²+P²/4-P×A).
4. If the radius of a circle (R) in which the rectangle is entered is known, then its diagonal will be equal to the doubled radius as the center of a rectangle and circle in this case coincide. The straight line which is connecting two points of a circle and passing through its center is equal to its diameter, that is two radiuses. And as tops of this rectangle lie on a circle, and the diagonal connecting them passes through the center, it corresponds to determination of diameter of a circle too: C=2×R.
5. If the radius of the circle (r) entered in a rectangle is known, then lengths of its parties are identical. This special case of a rectangle is called a square. It is possible to determine length of the parties in this case as the doubled circle radius length, and having substituted this expression in a formula from the first step, you receive: C= √ (4×r²+4×r²) =r× √ 8.