Question

If area of square is 96cm2 then its length of diagonal

Answer 1

Answer :-

given area of square is 96 cm^2

we know that

the area of square = a^2

${a}^{2} = 96$

$a = \sqrt{96}$

$a = 4 \sqrt{6}$

then

diagonal of square =

$\sqrt{ {(4 \sqrt{6)} }^{2} + {(4 \sqrt{6)} }^{2} }$

$= \sqrt{96 + 96}$

$= \sqrt{192}$

$= 8 \sqrt{3}$

therefore the length of diagonal is

8√3 cm

Answer 2

Concept: According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides. Look at the triangle ABC, where BC² = AB² + AC² is present. The base is represented by AB, the altitude by AC, and the hypotenuse by BC in this equation. It should be remembered that a right-angled triangle's hypotenuse is its longest side.

Given: The area of the square is 96 cm².

Find: Determine the length of diagonals.

Solution: The area of the square is 96 cm². Then

(side)²=96 cm²

$\implies \mbox{side} = \sqrt{96}=\sqrt{4\times 4\times 6} \\= 4\sqrt6$

⇒side = 4√6 cm

From the figure, we say that the two sides and diagonal 'd' make a right triangle and using Pythagoras theorem

$d^2=\mbox{side}^2+\mbox{side}^2$

$\implies d= \sqrt{2\times \mbox{side}^2}$

$\implies d= \sqrt{2\times 96} =8\sqrt{3}$ cm

Hence, the diagonal of the square is of length 8√3 cm

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