Question
If the length of the diagonal of a square is 20 cm, then its perimeter must be :
Answer: Option C
$$\eqalign{
& d = \sqrt 2 \times l \cr
& \Rightarrow l = \frac{{20}}{{\sqrt 2 }} \cr} $$
∴ Perimeter :
$$\eqalign{
& = \left( {4l} \right)cm \cr
& = \left( {\frac{{4 \times 20}}{{\sqrt 2 }} \times \frac{{\sqrt 2 }}{{\sqrt 2 }}} \right)cm \cr
& = 40\sqrt 2 \,cm \cr} $$
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$$\eqalign{
& d = \sqrt 2 \times l \cr
& \Rightarrow l = \frac{{20}}{{\sqrt 2 }} \cr} $$
∴ Perimeter :
$$\eqalign{
& = \left( {4l} \right)cm \cr
& = \left( {\frac{{4 \times 20}}{{\sqrt 2 }} \times \frac{{\sqrt 2 }}{{\sqrt 2 }}} \right)cm \cr
& = 40\sqrt 2 \,cm \cr} $$
Was this answer helpful ?
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