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2 years ago

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The length of a rectangle is 3 times twice the width. The perimeter is 36. What are the side lengths?

1 answer:

Svetllana [295]2 years ago

8 0

Answer & Explanation:

For this question, you need to figure out the length and the width because the area is directly related to them (A = l*w).

What we do know is that the perimeter is 36 inches. Since the perimeter is equal to P = 2l + 2w, we can say:

P = 36 = 2(3 + 2w) + 2(w), where the length l is 3 + 2w

Solve for w first, then solve for l. Use these values to find the area.

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In a group of eighteen people, each person shakes hands once with each other person in the group. How many handshakes will occur

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The number of handshakes that will occur in a group of eighteen people if each person shakes hands once with each other person in the group is 153 handshakes

In order to determine the number of handshakes that will occur among 18 people, that is, the number of ways we can choose 2 persons from 18 people.

∴ The number of handshakes = $^{18}C_{2}$

$^{18}C_{2} = \frac{18!}{(18-2)!2!}$

$^{18}C_{2} = \frac{18!}{16!2!}$

$^{18}C_{2} = \frac{18\times17\times16!}{16!\times2!}$

$^{18}C_{2} = \frac{18\times17}{2\times1}$

$^{18}C_{2} = \frac{306}{2}$

$^{18}C_{2} = 153$

∴ The number of handshakes = 153 handshakes

Hence. 153 handshakes will occur in a group of eighteen people if each person shakes hands once with each other person in the group.

Learn more here: brainly.com/question/1991469

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