Question

$\huge{\color{magenta}{\fbox{\textsf{\textbf{VERIFIED 亗}}}}}$ 1. The perimeter of a rhombus is 20 cm and one of its diagonal is 6 cm long . Find the length of other diagonal .​

Answer 1

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.

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Answer 2

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Rhombus is a parallelogram whose diagonals bisect each other.

So ,

Perimeter of rhombus = 20 cm

So measure of each side of rhombus = 20/4 = 5cm

One diagonal measures =6

So Half the diagonal measures = 6/2 = 3

So the other diagonal measures = [5² - 3²] ^1/2= 8cm

$\huge{\color{magenta}{\fbox{\textsf{\textbf{VERIFIED✅}}}}}$