Question

the area of a square is 50cm sq , then the length of its diagonal is​

Answer 1

Answer:

10cm sq

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Answer 2

Answer:

• Length of the diagonal of the square is 10 cm.

Step-by-step explanation:

Given that:

• Area of a square is 50 cm².

To Find:

• Length of the diagonal of the square.

As we know that:

$\sf{Area\;of \;square=\dfrac{1}{2}\times(diagonal)^2}$

Let us assume:

• Let the length of the diagonal of the square be d.

Substituting the values,

$\sf{\longmapsto50=\dfrac{1}{2}\times(d)^2}$

Transposing 1/2 from RHS to LHS and changing its sign,

$\sf{\longmapsto50\div\dfrac{1}{2}=(d)^2}$

$\sf{\longmapsto50\times2=(d)^2}$

Multiplying the numbers,

$\sf{\longmapsto100=(d)^2}$

Solving further,

$\sf{\longmapsto\sqrt{100}=d}$

$\sf{\longmapsto\sqrt{10\times10}=d}$

$\sf{\longmapsto10=d}$

Hence, length of the diagonal of the square is 10 cm.