If the diagonal of a square is twenty inches how do you find the length of the sides?

Answer 1

Fall back on Pythagoras.

d^(2) = a^(2) + b^(2)

Where 'd' is the diagonal, and 'a' & 'b' are the lengths of the two right angled sides.

However, being a square the sides are of equal length. Hence it follows that a = b

Hence a^(2) = b^(2)

So substitutiung

d^(2) = a^(2) + a^(2)

d^(2) = 2a^(2)

d = 20 as given

Then

d^(2) = 20^(2) = 400

Substituting

400 = 2a^(2)

a^(2) = 400/2 = 200

a^(2) = 200

Square rooting both sides.

a = sqrt(200) = sqrt(2 x 100) = sqrt(2) x sqrt(100) = sqrt(2) x 10 = 10sqrt(2)

10sqrt(2) numerically is 14.14213562....~ 14.14 inches.

Answer 2

You use the Pythagorean theorem. Remember that Asq + Bsq = Csquared, where A and B are the sides of a right triangle and C is the diagonal. (Remember that a right triangle is just a square cut in half slantwise.) Based on the theorem, you know that the sum of A squared and B squared equals 20 squared (20 squared = 20 x 20 or 400.) Also, since it's a square you concerned with, you know that the sides are the same length. So whatever length "A" side is, "B" side is the same. So we might as well say two times A is the same as A plus B. So two times A squared equals 400. We only want to know what ONE side of the square measures, so we can reduce both sides of the equation by dividing each side by 2. In other words, if TWO times A squared equals 400, then ONE times A squared equals 200. But we don't want to know what the length of A squared is, we want to know what the length of A is. So take the square root. A equals the square root of 200. The square root of 200 is fourteen plus a fraction. So your square is fourteen plus a fraction on each side. Check your work: 14 squared plus 14 squared = 196 + 196 = 392, which is is very close to the C squared we started with of 400. The square root of 400 is 20, and you are back to the beginning.