Find the perimeter of a rectangle if its diagonal is 5 cm and the smaller side is 3 cm as shown in the figure below.
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Solution
We know that in a rectangle, a diagonal divides a rectangle into two equal right-angled triangles as shown below.
So, if the diagonal is of 5 cm and one side of the right-angled triangle is 3 cm then via the knowledge of the Pythagorean triplet, we can directly say that the other side of the rectangle will be equal to 4 cm.
Therefore, if the length of the rectangle is 3 cm then its width will be 4 cm.
Hence its perimeter = 2 (L + B) = 2 (3 + 4) = 14 square units.