Question

question 2 points 2 find the length of the longest side of the rectangle whose dimensions are given by 2x and 5x -1, and has a perimeter of 26 feet. 4ft 6ft 9ft 10ft

Explanation:

Step1: Recall the perimeter formula for a rectangle.

The perimeter \( P \) of a rectangle with length \( l \) and width \( w \) is given by \( P = 2(l + w) \). Here, the dimensions are \( 2x \) and \( 5x - 1 \), and the perimeter \( P = 26 \) feet. So we set up the equation:
\[
2(2x + (5x - 1)) = 26
\]

Step2: Simplify the left - hand side of the equation.

First, simplify the expression inside the parentheses: \( 2x+(5x - 1)=2x + 5x-1 = 7x-1 \). Then the equation becomes:
\[
2(7x - 1)=26
\]
Distribute the 2: \( 14x-2 = 26 \)

Step3: Solve for \( x \).

Add 2 to both sides of the equation:
\[
14x-2 + 2=26 + 2
\]
\[
14x=28
\]
Divide both sides by 14:
\[
x=\frac{28}{14}=2
\]

Step4: Find the lengths of the sides.

For the first side with length \( 2x \), substitute \( x = 2 \): \( 2x=2\times2 = 4 \) feet.
For the second side with length \( 5x - 1 \), substitute \( x = 2 \): \( 5x-1=5\times2-1=10 - 1 = 9 \) feet.

Step5: Determine the longest side.

Compare the two side lengths: 4 feet and 9 feet. The longer side is 9 feet.

Answer:

9 ft