hey mate ^_^
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the perimeter of a rhombus is 20 m and one of its diagonal has a length of 6 cm. Find the length of its other diagonal
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thnx : )
Answers
Solution :
Given perimeter of rhombus = 20 cm
Let the equal side of the rhombus be k
Perimeter of rhombus = 4k
That is 4k = 20
k = 20/4 = 5
Therefore the side of rhombus, k = 5 cm
Given length of one of the diagonal, AC = 8 cm
Recall that the diagonals bisect each other at right angles in a rhombus
Thus OA = 4 cm
In right ΔAOD
By Pythagoras theorem, we have AD2 = OA2 + OD2
52 = 42 + OD2
25 - 16 = OD2
OD2 = 9
OD = 3 cm
Length of other diagonal BD = 2 x OD
= 2 x 3 cm = 6 cm
#MathsAryabhatta
Answer:
Perimeter = 20 cm.
Since all sides of the rhombus are equal, so each side of the rhombus= 20 cm/4 = 5 cm.
The diagonals of a rhombus bisect each other at right angle. Therefore, the diagonals divide the rhombus in 4 equal right triangles, whose hypotenuse are the sides of the rhombus, and other two sides are the half lengths of the two diagonals.
In one such right triangle, hypotenuse = 5 cm, side 1 = 6 cm/2 = 3 cm
Therefore, side 2 of the right triangle= [ 5² -3²]½= 4 cm.
Therefore length of the second diagonal = 2×4 cm = 8 cm.
Hope it's Helpful for you....