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tankabanditka [31]
3 years ago
13

The length of a rectangle is two more than triple the width if the perimeter is 148inches find the dimensions

Mathematics
1 answer:
gayaneshka [121]3 years ago
5 0

Answer:

width = 18 inches

length = 56 inches

Step-by-step explanation:

Let x = width

Let y = length

<u>Equation 1</u>

If length of the rectangle is 2 more than triple the width, then:

⇒ y = 3x + 2

<u>Equation 2</u>

Perimeter of a rectangle = 2(width + length)

If the perimeter is 148 inches, then:

⇒ 148 = 2(x + y)

<u>Solve by substitution</u>

Substitute Equation 1 into Equation 2 and <u>solve for x</u>:

⇒ 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 <u>solve for y</u>:

⇒ y = 3(18) + 2

⇒ y = 54 + 2

⇒ y = 56

<u>Conclusion</u>

The dimensions of the rectangle are:

  • width = 18 inches
  • length = 56 inches
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