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Chapter 2: Problem 41

The length of a side of a square is \(5 l^{2}\) units. a) Write an expression for its perimeter. b) Write an expression for its area.

Short Answer

Expert verified
a) Perimeter: \(20l^2\) units b) Area: \(25l^4\) square units

Step by step solution

01

1. Calculate the perimeter of the square

Since all sides of a square are equal, to find the perimeter, simply multiply the given side length by 4. The length of a side is: \(5l^2\) Perimeter (P) = 4 脳 side length = 4 脳 (5\(l^2\))
02

2. Simplify the expression for perimeter

To obtain the final expression for the perimeter, perform the multiplication: Perimeter (P) = 4 脳 (5\(l^2\)) = 20\(l^2\) Hence, the perimeter of the square is \(20l^2\) units.
03

3. Calculate the area of the square

To find the area of a square, multiply the length of a side by itself: Length of a side is: \(5l^2\) Area (A) = side length 脳 side length = (5\(l^2\)) 脳 (5\(l^2\))
04

4. Simplify the expression for the area

To obtain the final expression for the area, perform the multiplication: Area (A) = (5\(l^2\)) 脳 (5\(l^2\)) = 25\(l^4\) Hence, the area of the square is \(25l^4\) square units.

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Most popular questions from this chapter

Perform the operation as indicated. Write the final answer without an exponent. \(\frac{2 \times 10^{1}}{5 \times 10^{4}}\)

Simplify the expression using one of the power rules. $$\left(x^{4}\right)^{3}$$

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