Diagonals AC and BD of a rectangle ABCD intersect each other at point o.If DA=3cm.Find AC and BD.
10cm
To find the lengths of the diagonals AC and BD of the rectangle, we can use the properties of rectangles.
Given that DA = 3 cm, we can see that triangle ADO is a right triangle. Let's label the point of intersection as O.
Using the Pythagorean theorem, we can find the length of the diagonal AC:
AC^2 = AD^2 + DC^2
AC^2 = 3^2 + DC^2
AC^2 = 9 + DC^2
To find DC, we need to use the fact that opposite sides of a rectangle are congruent. Therefore, DC = AB.
Let's assume AB = x cm (since we don't know its value yet).
AC^2 = 9 + x^2
AC = √(9 + x^2)
Next, we can use the fact that diagonals of a rectangle are equal in length. Therefore, AC = BD.
So, BD = √(9 + x^2) cm.
To find the exact values of AC and BD, we need to know the length of the other side of the rectangle (AB). If you provide the length of AB, we can calculate the values of AC and BD.