Question
Find the side and perimeter of a square whose diagonal is 10 cm.
✓
Answer
In a square of side say a cm, any diagonal divide the square into two right triangles of equal dimensions.
Thus $a^2+a^2=10^2$
$\Rightarrow 2 a^2=100$
$\Rightarrow a^2=50$
$a=5 \sqrt{2} \mathrm{~cm}$
a = 5$\sqrt 2$ cm
perimeter = 4a
= 4×5$\sqrt 2$
= 20$\sqrt 2$
Perimeter of square = 20$\sqrt 2$cm
Thus $a^2+a^2=10^2$
$\Rightarrow 2 a^2=100$
$\Rightarrow a^2=50$
$a=5 \sqrt{2} \mathrm{~cm}$
a = 5$\sqrt 2$ cm
perimeter = 4a
= 4×5$\sqrt 2$
= 20$\sqrt 2$
Perimeter of square = 20$\sqrt 2$cm
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