the area of a square is 49 square inches. find the number of inches in the length of a diaganol. express your answer in simplest radical form.
what in the world
A=side^2
49=s^2
s=7
Pythagorean Theorem
d=sqrt(2times7^2)
d=7squareroot2 = 7√2
To find the length of the diagonal of a square given its area, we first need to find the length of its sides.
Given that the area of the square is 49 square inches, we know that the area of a square is equal to the length of one of its sides squared.
Let's call the length of one side of the square "s". So we can write the equation:
s^2 = 49
To find the length of the side, we take the square root of both sides of the equation:
sqrt(s^2) = sqrt(49)
s = 7
Now that we know the length of one side of the square is 7 inches, we can find the length of the diagonal.
In a square, the length of the diagonal forms a right triangle with the sides of the square. The diagonal acts as the hypotenuse, and the sides of the square act as the legs of the right triangle.
Using the Pythagorean theorem, we can find the length of the diagonal (d) as follows:
d^2 = s^2 + s^2 (by Pythagorean theorem)
d^2 = 7^2 + 7^2
d^2 = 49 + 49
d^2 = 98
Taking the square root of both sides of the equation, we can solve for d:
sqrt(d^2) = sqrt(98)
d = sqrt(98)
Now, we simplify the radical form of sqrt(98):
d = sqrt(49 * 2)
d = sqrt(49) * sqrt(2)
d = 7 * sqrt(2)
Therefore, the length of the diagonal is 7sqrt(2) inches.