The diagonal of a quadilateral are of the lengths 10cm and 24cm.if the diagonals bisect each other at right angels,find the length of each side of d quadilateral.what special name can you give to this quadiletral?
You have 4 congruent right-angled triangles
let the side be x
x^2 = 5^2+6^2 = 61
x=√61 , that being the length of each of the four sides
the quad is a rhombus
Plz gve me clr soltn it ans is 13cm
To find the lengths of the sides of the quadrilateral, we can use the properties of a quadrilateral with perpendicular diagonals.
In a quadrilateral with perpendicular diagonals, the diagonals divide the quadrilateral into four right-angled triangles. Using the Pythagorean theorem, we can find the lengths of the sides.
Let's call the lengths of the sides of the quadrilateral a, b, c, and d. Based on the given information, we know that the diagonals divide the quadrilateral into two congruent right-angled triangles.
Applying the Pythagorean theorem to one of these triangles, we have:
(a/2)^2 + (b/2)^2 = 10^2 ----(1)
(c/2)^2 + (d/2)^2 = 24^2 ----(2)
Expanding equations (1) and (2):
(a^2 + b^2)/4 = 100 ----(3)
(c^2 + d^2)/4 = 576 ----(4)
Now, we need to find a relation between the lengths of the sides. Since the diagonals bisect each other, the quadrilateral is a parallelogram. In a parallelogram, opposite sides are congruent.
Thus, a = c and b = d.
Substituting these values into equations (3) and (4), we have:
(a^2 + b^2)/4 = 100 ----(5)
(a^2 + b^2)/4 = 576 ----(6)
Now, we can solve equations (5) and (6) simultaneously by equating them:
100 = 576
As these two equations contradict each other, it means there is no solution for the lengths of the sides of the quadrilateral with diagonal lengths 10 cm and 24 cm that bisect at right angles.
Therefore, there is no particular name for this quadrilateral, as it does not satisfy the given conditions.