Answer:
22 meters
Step-by-step explanation:
Let x = width of the rectangle
Let y = length of the rectangle
<u>Equation 1</u>
If the length of the rectangle is 6 meters shorter than four times the width then:
⇒ y = 4x - 6
<u>Equation 2</u>
Perimeter of a rectangle = 2(width + length)
If the perimeter is 58 inches, then:
⇒ 58 = 2(x + y)
<u>Solve by substitution</u>
Substitute Equation 1 into Equation 2 and <u>solve for x</u>:
⇒ 58 = 2(x + 4x - 6)
⇒ 58 = 2(5x - 6)
⇒ 58 = 2 · 5x - 2 · 6
⇒ 58 = 10x - 12
⇒ 58 + 12 = 10x -12 + 12
⇒ 10x = 70
⇒ 10x ÷ 10 = 70 ÷ 10
⇒ x = 7
Substitute found value of x into Equation 1 and <u>solve for y</u>:
⇒ y = 4(7) - 6
⇒ y = 28 - 6
⇒ y = 22
<u>Conclusion</u>
The dimensions of the rectangle are:
- width = 7 meters
- length = 22 meters
Therefore, the length of the longer side is 22 meters