Answer:
width = 18 inches
length = 56 inches
Step-by-step explanation:
Let x = width
Let y = length
Equation 1
If length of the rectangle is 2 more than triple the width, then:
⇒ y = 3x + 2
Equation 2
Perimeter of a rectangle = 2(width + length)
If the perimeter is 148 inches, then:
⇒ 148 = 2(x + y)
Solve by substitution
Substitute Equation 1 into Equation 2 and solve for x:
⇒ 148 = 2(x + 3x + 2)
⇒ 148 = 2(4x + 2)
⇒ 148 = 2 · 4x + 2 · 2
⇒ 148 = 8x + 4
⇒ 148 - 4 = 8x + 4 - 4
⇒ 8x = 144
⇒ 8x ÷ 8 = 144 ÷ 8
⇒ x = 18
Substitute found value of x into Equation 1 and solve for y:
⇒ y = 3(18) + 2
⇒ y = 54 + 2
⇒ y = 56
Conclusion
The dimensions of the rectangle are:
- width = 18 inches
- length = 56 inches
