The perimeter of a rhombus is 52m and its shorter diagonal is 10m. The length of the longer diagonal is-

Explanation

Each sides of rhombus = $\frac{52}{4} = 13$ m Let, the length of longer diagonal of rhombus is $2x$ m. Since half of both diagonal and one side form a right angled triangle, whose hypotenuse is the side of the rhombus. So, $\left(\frac{10}{2}\right)^2 + \left(\frac{2x}{2}\right)^2 = (13)^2$ $(5)^2 + (x)^2 = 169$ $x^2 = 169 - 25$ $x = \sqrt{144} = 12$ m So, the length of longer diagonal of rhombus = (2 × 12) m = 24 m