Mathematics 2019 JAMB Past Questions - Question 33: . Find the length of a side of a rhombus whose diagonals are 6cm and 8cm

Correct Answer

B

Explanation

The diagonals of a rhombus bisect each other at right angles and are of equal length. This means that the diagonals divide the rhombus into four congruent right-angled triangles. We can use the Pythagorean theorem to find the length of each side of the rhombus.Let's denote the length of the diagonals as \( d_1 \) and \( d_2 \), and the length of each side as \( s \). Then, the Pythagorean theorem gives us:\[ \left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2 = s^2 \]Substituting the given values \( d_1 = 6 \, \text{cm} \) and \( d_2 = 8 \, \text{cm} \) into the equation gives:\[ \left(\frac{6}{2}\right)^2 + \left(\frac{8}{2}\right)^2 = s^2 \]\[ 3^2 + 4^2 = s^2 \]\[ 9 + 16 = s^2 \]\[ 25 = s^2 \]Taking the square root of both sides gives:\[ s = 5 \, \text{cm} \]So, the length of each side of the rhombus is 5 cm.