question_answer

The area of a rhombus whose one side and one diagonal measure 20 cm and 24 cm respectively is

A)  \[364\,\,\text{c}{{\text{m}}^{2}}\]

B)  \[374\,\,\text{c}{{\text{m}}^{2}}\]

C)  \[384\,\,\text{c}{{\text{m}}^{2}}\]

D)  \[394\,\,\text{c}{{\text{m}}^{2}}\]

Correct Answer: C

Solution :

Let   the   other   diagonal   be   2x.   So, in \[\Delta AOB,\]\[{{(20)}^{2}}={{(12)}^{2}}+{{x}^{2}}\] \[\Rightarrow \]\[{{x}^{2}}=400-144\] \[\Rightarrow \]   \[{{x}^{2}}=256\]\[\Rightarrow \]\[x=16\,\,\text{cm}\] \[\therefore \] Other diagonal \[=2x=32\,\,\text{cm}\] \[\therefore \]      \[\text{Area}=\frac{1}{2}\times {{d}_{1}}{{d}_{2}}\] \[=\frac{1}{2}\times 24\times 32=384\,\,\text{c}{{\text{m}}^{2}}\]