Use the image to answer the question.
An illustration of a rectangular prism is shown with labeled parts. The top, front and right sides are visible. The bottom, left, and rear sides are not visible, but their positions are indicated by dashed lines. The vertical edge joining the front and left sides shows a height of 12 centimeters. The front base edge shows a width of 3 centimeters. The right base edge shows a length of 4 centimeters. A dotted line extends diagonally from the vertex at the bottom back right side of the prism through the interior of the prism to the vertex at the top front left.
Find the length of the diagonal of the prism.
(1 point)
cm
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To find the length of the diagonal of the prism, we can 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 can see that the diagonal forms a right-angled triangle with the height, width, and length of the prism. Let's call the length of the diagonal "d".
Using the Pythagorean theorem, we can set up the equation:
d^2 = height^2 + width^2 + length^2
From the information given in the problem, we know that the height is 12 cm, the width is 3 cm, and the length is 4 cm.
Plugging these values into the equation, we get:
d^2 = 12^2 + 3^2 + 4^2
Simplifying, we get:
d^2 = 144 + 9 + 16
d^2 = 169
Taking the square root of both sides, we get:
d = √169
Therefore, the length of the diagonal of the prism is 13 cm.
The length of the diagonal of the prism can be found using the Pythagorean theorem. The vertical edge joining the front and left sides, the front base edge, and the right base edge form a right triangle. We can use the Pythagorean theorem to find the length of the diagonal.
The height of the prism (vertical edge) is given as 12 centimeters, the width (front base edge) is given as 3 centimeters, and the length (right base edge) is given as 4 centimeters.
Using the Pythagorean theorem, we have:
diagonal^2 = height^2 + width^2 + length^2
diagonal^2 = 12^2 + 3^2 + 4^2
diagonal^2 = 144 + 9 + 16
diagonal^2 = 169
Taking the square root of both sides, we get:
diagonal = √169
diagonal = 13 centimeters
Therefore, the length of the diagonal of the prism is 13 centimeters.
To find the length of the diagonal of the prism, we can use the Pythagorean theorem. The diagonal of a rectangular prism forms a right triangle with the width, length, and height as its sides.
We are given that the width is 3 centimeters, the length is 4 centimeters, and the height is 12 centimeters.
Using the Pythagorean theorem, we can find the length of the diagonal, which is the hypotenuse of the right triangle.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
So, we have:
c^2 = a^2 + b^2
c^2 = 3^2 + 4^2
c^2 = 9 + 16
c^2 = 25
Taking the square root of both sides to solve for c, we have:
c = √25
c = 5
Therefore, the length of the diagonal of the prism is 5 centimeters.