Question

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.

Answer 1

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.