Which is closest to the length of the diagonal of a square whose sides measure 20 cm?
a.20 cm
b.28 cm
c.40 cm
d.200 cm
Which do you think is the right answer?
20^2 + 20^2 = c^2
The square on the hypotenuse us equal to the sum of the squares on the other two sides....
So square the sides to figure out the square on the diagonal side, then you can work out the length of that side.
40
40 cm
To find the length of the diagonal of a square, 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 other two sides.
In this case, the sides of the square measure 20 cm. Let's call the length of the diagonal "d". We can divide the square into two right triangles by drawing a diagonal. Each right triangle will have a leg of length 20 cm.
Using the Pythagorean theorem, we can write the equation:
d^2 = 20^2 + 20^2
Simplifying:
d^2 = 400 + 400
d^2 = 800
Taking the square root of both sides:
d = √800 ≈ 28.28 cm
Therefore, the length of the diagonal of the square is closest to 28 cm. So, the answer is (b) 28 cm.