Question

What is the length of the diagonal AC of square ABCD given that AB = 8 cm ?​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given : A square ABCD having side $AB=8cm$ .

To find : The length of diagonal AC of square.

Formula used : We use Pythagoras theorem to find the diagonal (H),

$H^{2} =P^{2} +B^{2}$

$H=\sqrt{P^{2} +B^{2} }$

H if for Hypotenuse, B is the base and P is the perpendicular of right angled triangle.

• Calculation for the length of AC

As we know that all four angles of a square are $90\°$ so with the diagonal square form a right angled triangle $\triangle ABC$ that's why we use Pythagoras theorem here. All sides of square are same and side of square is,

$AB=8cm$

For the  $\triangle ABC$,

AB is the perpendicular (P) , BC is Base (B) and AC is Hypotenuse(H). so the,

$P=8cm$

$B=8cm$

by using formula,

$H=\sqrt{P^{2} +B^{2} }$

     $=\sqrt{(8)^{2} +(8)^{2}}$

     $=\sqrt{64+64}$

    $=\sqrt{128}$

We can write 128 as $128=64*2$

$H=\sqrt{64*2}$

and the $\sqrt{64}=8$

so , $H=8\sqrt{2}$

We get the length of diagonal AC is $8\sqrt{2}$ cm.