Question

Find the length of the diagonal of a square of side is 7√2 cm

Answer 1

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Given :- Length of side of ◻ABCD square is 7√2 cm.
AD = DC = CB = BA = 7√2. ---- ( All side of square are have same measure )

To Find :- Length of diagonal ( BD ) and ( AC ).
BD = AC ------ ( Diagonal of square are congruent )

Solution :- In ∆ABD , Angle BAD = 90

( All angle are 90 as ◻ABCD is square.)
Hence,
AD^2 + AB^2 = BD^2
BD^2 = ( 7√2 )^2 + ( 7√2 )^2
BD^2 = 98 + 98
BD^2 = 196
BD = √196
BD = 14 cm

As we know BD = AC are diagonals of ◻ABCD

so, length of diagonal is 14 cm.

Answer 2

Given:

The length of a side of a square is 7√2 cm.

To Find:

The length of the diagonal of the square is?

Solution:

The given problem can be solved using the concepts of Squares.

1. The side length of the square is 7√2 cm.

2. Consider a square of side A units. The length of the diagonal of the square is given by the formula,

=> Length of the diagonal = A√2 Units.

3. Using the formula mentioned above, the diagonal length can be calculated,

=> The length of the diagonal = 7√2 x √2 cm,

=> Length of the diagonal = 7 x 2 cm,

=> Length of the diagonal = 14cm.

Therefore, the length of the diagonal is 14cm.