a group of boys in a camp wanted to set up a tent. theslanted sides are both 2.5 metres long and the bottomof the tent is 3 metres across. what is the height ofthe tent, in metres, at its tallest point?

The tent is in the shape of a triangular prism, where the slanted sides can be considered as the height of the prism. To find the height, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the other two sides squares.

In this case, the hypotenuse is the height of the tent, one side is the length of the slanted side (2.5 meters), and the other side is half of the bottom of the tent (1.5 meters).

Using the Pythagorean theorem, we can calculate:

height² = slanted side² - (1/2 * bottom)²

height² = 2.5² - (1.5²)

height² = 6.25 - 2.25

height² = 4

Taking the square root of both sides, we find that the height of the tent is 2 meters at its tallest point.

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