Point Q belongs to side AB of square ABCD. The distances from point Q to the diagonals of the square are 2 ft and 3 ft. Find the diagonal of the square.
both of them are 10, AC=10, BD=10
wait, so the diagonal is 5, or 5 times 2
5 x 2 = 10
AC = 10
what's AC
10 for both
it is 10 for both lmao
Yeah the diagonal is 10
To solve this problem, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's denote the length of the diagonal of the square as d.
From the given information, we know that the distance from point Q to one diagonal is 2 ft, and the distance from point Q to the other diagonal is 3 ft.
We can consider the triangle formed by connecting point Q to the two endpoints of one of the diagonals. This triangle is a right triangle because both diagonals of a square intersect at a right angle.
Using the Pythagorean Theorem, we can write the equation:
2^2 + (d)^2 = 3^2
Simplifying this equation, we get:
4 + d^2 = 9
Subtracting 4 from both sides:
d^2 = 9 - 4
d^2 = 5
Taking the square root of both sides to solve for d:
d = sqrt(5)
Therefore, the length of the diagonal of the square is sqrt(5) ft.