Question

The area of a square is 32 m². Its each diagonal has a length of?​

Answer 1

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The formula for the area of a square is:

A = s², where s is the length of one of the 4 congruent sides of the square.

The relationship between the length d of either diagonal of a square and the length s of a side of the square is given by the formula: d = s√2, where d is the length of one of the two congruent diagonals of the square. Since we're given that the diagonal length d of the square is 32, we'll substitute this information into the formula for d to find s, and then we'll be able to find the area A of the square as follows:

d = s√2

32 = s√2

32/√2 = (s√2)/√2

32/√2 = s(√2/√2)

32/√2 = s(1)

s = 32/√2

Now, rationalizing the denominator for s so as to make the value for s easier to work with, we get:

s = (32/√2)(1)

= (32/√2)(√2/√2)

= (32√2)/(√2√2)

= (32√2)/√4

= (32√2)/2

= (32/2)√2

s = 16√2

Now, substituting for s into the formula for the area A of a square, we have:

Now, substituting for s into the formula for the area A of a square, we have:A = s²

= (16√2)²

= (16)²(√2)²

= (16)(16)(√2)(√2)

= 256(√2)(√2)

= 256(√4)

= 256(2)

A = 512 square units is the area of the square whose diagonal is 32.