Chapter 10.2, Problem 36P

You are making a mosaic design on a square table top. You have already covered half of the table top with 150 1-inch square tile pieces.

1. What are the dimensions of the table top?
2. What is the measure of the diagonal from one corner to the opposite corner of the tabletop?

To determine

To find the dimension of the table top.

Answer to Problem 36P

The sides of the square table top is $10\sqrt{3}in.$

Explanation of Solution

Given information:

The given statement is:

“You are making a mosaic design on a square table top. You have already covered half of the table top with $150\text{ 1-inch}$ square tile pieces.”

Calculation :

The area of half of the table top is:

$\left(150\times 1\right)in{.}^2=150in{.}^2$

The area of the full table top is:

$150in{.}^2\times 2=300in{.}^2$

The dimension of the table top is:

$\begin{array}{l}side=\sqrt{area}\\ side=\sqrt{300}\\ side=10\sqrt{3}in.\end{array}$

Hence, the sides of the square table top is $10\sqrt{3}in.$

To determine

To find the measure of the diagonal from one corner to the opposite corner of the table top.

Answer to Problem 36P

The length of the diagonal is $10\sqrt{6}in.$

Explanation of Solution

Given information:

The given statement is:

“You are making a mosaic design on a square table top. You have already covered half of the table top with $150\text{ 1-inch}$ square tile pieces.”

Calculation :

The diagonal can be calculated by:

$\begin{array}{l}{d}^2={\left(10\sqrt{3}\right)}^2+{\left(10\sqrt{3}\right)}^2\\ d^2=300+300\\ d=\sqrt{600}\\ d=10\sqrt{6}\end{array}$

Hence, the length of the diagonal is $10\sqrt{6}in.$