Question

The diagonal of a square is 10 cm. What is the length (in cm) of its side?

A) 5 B) 5√2 C) 10√2 D) 5/√2

Answer 1

✰ ANSWER ✰

• B) 5√2 (✔)

GIVEN:

• Diagonal of a square(AC) = 10 cm

TO FIND:

• What is the side of the square ?

SOLUTION:

Let the side of the square be 'x' cm

Since,

All sides of a square are equal in length.

To find the length of the side of a square, we use Pythagoras theorem:-

$\bf{\star \: (Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2\: \star}$

• Hypotenuse = 10 cm
• Base = x cm
• Perpendicular = x cm

According to question:-

On putting the given values in the formula, we get

$\rm{\dashrightarrow (10)^2 = (x)^2 + (x)^2}$

$\rm{\dashrightarrow 100 = 2x^2 }$

$\rm{\dashrightarrow \cancel\dfrac{100}{2} = x^2 }$

$\rm{\dashrightarrow 50 = x^2}$

$\rm{\dashrightarrow \sqrt{50} = x }$

$\rm{\dashrightarrow \sqrt{2 \times 5 \times 5} = x }$

$\bf{\dashrightarrow 5 \sqrt{2} = x }$

❝ Hence, the side of an square is 5√2 cm ❞

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Answer 2

$5 \sqrt{2} \: is \: the \: answer \\ \huge \: thank \: you$