Learn what is the formula for diagonal of rectangle in math. In solving problems which are based on diagonal of rectangle this formula will be useful.
Regarding rectangle, we have mainly three formulas that we need to learn without neglecting. The three formulas are first one is area of rectangle formula, second one is perimeter of rectangle formula and third one formula for diagonal of rectangle. First two formulas i think everyone knows. So now we will discuss third formula. Not only the formula first we will discuss what is the meaning of diagonal, whether the diagonal equal or not and then finally the formula for finding the diagonal.
What is the meaning of “diagonal” in math?
We know that in a quadrilateral or in a polygon there will be vertices. Suppose if it is a quadrilateral there will be four vertices and if it is pentagon there will be five vertices, for hexagon six vertices and so on. Rectangle comes under quadrilateral. So for a rectangle there will be four vertices. Now the meaning of diagonal is “the line segment formed by joining two non adjacent vertices is called as diagonal”. So totally we get two diagonals for a rectangle.
Are the two diagonals of a rectangle are equal in the measurement?
Just know we discussed that for a rectangle there will be two diagonals. Now the doubt is whether the two diagonals are equal or not equal. Remember that in a rectangle both the diagonals will be of equal in measurement.
The Formula used for finding the diagonal of a rectangle?
For knowing what is the formula for diagonal of rectangle, we first consider a rectangle PQRS. In this rectangle we have tow diagonals i.e. PR and QS. As both diagonals are equal so knowing formula for any one diagonal is enough.
Observe the triangle PQR, what kind of triangle it is? The triangle is a right angled triangle. We know that for a right angled triangle we can apply the Pythagoras theorem. So according to that we can write as
PR2 = PQ2 + QR2
= a2 + b2
Therefore PR, the diagonal of rectangle = √a2 + b2