Question

The area of canvas required to make a tent in the shape of a squared base pyramid is 14400 cm². If its slant height to vertical height ratio is 5:3, then for how many people can the seats be arranged inside the tent if each person needs 32 cm² of place on the ground?

a) 270
b) 300
c) 330
d) 360

Answer 1

Given that the area of the tent's base is 14400 cm² and the slant height to vertical height ratio is 5:3, we can find the vertical height of the tent using the Pythagorean theorem. The tent can accommodate 450 people.

Step-by-step explanation:

To find the number of seats that can be arranged inside the tent, we need to find the area of the tent's base and then divide it by the area needed for each person.

Given that the area of the tent's base is 14400 cm² and the slant height to vertical height ratio is 5:3, we can find the vertical height of the tent using the Pythagorean theorem.

Let's assume the vertical height of the tent is 3x. Then, the slant height would be 5x. Using the Pythagorean theorem: (3x)² + x² = (5x)². Simplifying this equation gives us: 10x² = 9x². Solving for x, we get x = 0.9 cm.

Now, we can find the vertical height by multiplying x by 3: vertical height = 3 * 0.9 cm = 2.7 cm.

Next, we divide the area of the tent's base by the area needed for each person: 14400 cm² / 32 cm² = 450.

Therefore, the tent can accommodate 450 people.