# another math question?

the diagonal of a square is 5 square root 14 what is the area of the square

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• The diagonal of a square cuts the square into 2 right triangles,

each with with angles measuring 45°-90°-45°.

These types of triangles carry a special ratio between sides:

.....leg1:hypotenuse:leg2 = 1:√2:1

So if the diagonal is 5√14, then

..........................5√14

.....leg1 = leg2 = ------ = 5√7

...........................√2

and the area of the square is (5√7)² = 25(7) = 175...........ANS • The area of a square is one-half the square of a diagonal. This simple formula is possible because the diagonals of a square are perpendicular and equal in length.

[5√(14)]²/2 = 175

• Area of Square = ½ × d^2

The diagonal of a square is 5√14

The area of the square = ((5√14)^2) / 2  = 175

• Anonymous
8 months ago

For an equilateral right triangle, the hypotenuse is the length of the side multiplied by the square root of 2. So the length of the side is:

x(square root of 2) = 5(square root of 7)

x = 5square root 7

Area = x^2

(5(square root 7))^2 = 25 * 7 = 175