Question

If the diagonals of a rhombus are 12 cm and 16cm, find the length of each side.

 

 

Answer 1

\[\text{ All sides of a rhombus are equal in length }. \]
\[\text{ The diagonals intersect at 90\textdegree and the sides of the rhombus form right triangles } . \]
\[\text{ One leg of these right triangles is equal to 8 cm and the other is equal to 6 cm } . \]
\[\text{ The sides of the triangle form the hypotenuse of these right triangles }. \]
\[\text{ So, we get }: \]
\[( 8^2 + 6^2 ) {cm}^2 \]
\[ = (64 + 36) {cm}^2 \]
\[ = 100 {cm}^2 \]
\[\text{ The hypotneuse is the square root of 100 {cm}^2 . This makes the hypotneuse equal to 10 }. \]
\[\text{ Thus, the side of the rhombus is equal to 10 cm } .\]