Question

the area of a rhombus is 184cm^2 & its perimeter is 64cm.
find its altitude.

Answer 1

$\mathsf \red{ Given\: } \\ \\ \mathsf{perimeter \: of \: rhombus \: = \: 64 \: cm} \\ \\ \boxed{\mathsf \blue{perimeter \: of \: rhombus \: = 4 \times side}} \\ \\ \mathsf{4 \times side \: = \: 64 \: cm} \\ \\ \mathsf{side \: (s) \: = \: \frac{64}{4} = 16 \: cm } \\ \\ \mathsf \red{hence, \: base \: of \: rhombus \: = \: 16 \: cm} \\ \\ \mathsf{area \: of \: rhombus \: = \: 184 \: {cm}^{2} \: \: \: \: \: } \\ \\ \boxed{ \mathsf \blue{area \: of \: rhombus \: = \: s \times h}} \\ \\ \mathsf{16 \times h \: = \: 184 \: } \\ \\ \mathsf{ h = \frac{184}{16} = 11.5 \: cm} \\ \\ \boxed{\mathsf \red{ \therefore \: \: altitude \: of \: rhombus \: = \: 11.5 \: cm}}$

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