Question

You would first use the Pythagorean Theorem on the bottom of the box rectangle to find the diagonal CB = 5 cm

Then use CB as of the triangle ACB, with AB being the hypotenuse .

AB is approximately = 13 cm

Answer 1

[AI-generated answer — Explain Bot]

To find the length of the diagonal CB of the rectangle, you would use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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, we know that the length of one side of the rectangle is 3 cm, and the width is 4 cm. To find the length of the diagonal CB, we can use the Pythagorean theorem as follows:

CB^2 = 3^2 + 4^2
CB^2 = 9 + 16
CB^2 = 25

Taking the square root of both sides, we find that:

CB = √25
CB = 5 cm

So the length of the diagonal CB is 5 cm.

Now, let's move on to finding the length of the hypotenuse AB of the triangle ACB. In this triangle, AB is the hypotenuse, and CB is one of the other sides. We already know that CB = 5 cm.

To find the length of AB, we can again use the Pythagorean theorem:

AB^2 = AC^2 + CB^2

Since AC is the remaining side of the triangle, we need to find its length. Since AC and the width of the rectangle are parallel, we can consider AC as the length of the rectangle, which is 3 cm.

Substituting the values into the Pythagorean theorem, we get:

AB^2 = 3^2 + 5^2
AB^2 = 9 + 25
AB^2 = 34

Taking the square root of both sides, we find:

AB = √34

So the length of the hypotenuse AB is approximately 5.83 cm.

Therefore, the length of the diagonal CB is 5 cm, and the length of the hypotenuse AB is approximately 5.83 cm.