Question

Find the perimeter of a rhombus, the lengths of whose diagonals are 16cm and 30cm.

Answer 1

$\mathsf \red{Given} \\ \\ \mathsf{diagonal \: of \: rhombus \: (d_{1}) \: = \: 16 \: cm} \\ \\ \mathsf{diagonal \: of \: rhombus \: (d_{2}) \: = \: 30 \: cm} \\ \\ \boxed{ \boxed{ \mathsf \red{let \: us \: find \: the \: side \: of \: the \: rhombus}}} \\ \\ \mathsf{from \: \triangle \: AOC \: : } \\ \\ \mathsf{{AO}^{2}+{OC}^{2} \: = \: {AC}^{2}} \\ \\ \mathsf{{16}^{2}+{30}^{2} \: = \: {AC}^{2}} \\ \\ \mathsf{256 + 900 \: = \: {AC}^{2}} \\ \\ \mathsf{1156 = \: {AC}^{2}} \\ \\ \mathsf{AC \: = \: \sqrt{1156} } \\ \\ \boxed{ \mathsf{AC \: = \: 34}} \\ \\ \mathsf{ \therefore \: one \: side \: is \: 34 \: cm} \\ \\ \boxed{ \mathsf \blue{perimeter \: = \: 4 \times side}} \\ \\ \mathsf{perimeter \: = \: 4 \times 34} \\ \\ \boxed{\mathsf\red{perimeter \: = \: 136 \: cm}}$

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