Question

The width of a rectangle measures (3.2t + 5.8) centimeters, and its length measures (1.8t - 3.8) centimeters. What expression represents the perimeter, in centimeters, of the rectangle?

a) 2(3.2t + 5.8) + 2(1.8t - 3.8)
b) 2(3.2t + 1.8t) + 2(5.8 - 3.8)
c) 3.2t + 5.8 + 1.8t - 3.8
d) 2(3.2t - 5.8) + 2(1.8t + 3.8)

Answer 1

The expression representing the perimeter of the rectangle is found using the formula P = 2l + 2w. By substituting the given expressions for the width and length into the formula, we get P = 2(3.2t + 5.8) + 2(1.8t - 3.8), which is answer option a).

Step-by-step explanation:

The student is given the width and length of a rectangle in terms of t, and they need to find an expression representing the perimeter of the rectangle. The perimeter of a rectangle is calculated by adding together twice the width and twice the length. In mathematical terms, this formula is expressed as P = 2l + 2w, where P is the perimeter, l is the length, and w is the width of the rectangle.

To find the expression for the perimeter in terms of t, we plug in the given expressions for width (w = 3.2t + 5.8 cm) and length (l = 1.8t - 3.8 cm) into our perimeter formula, yielding: P = 2(3.2t + 5.8) + 2(1.8t - 3.8). Simplifying this expression gives us the perimeter of the rectangle in terms of t.

Therefore, the correct answer to the question 'What expression represents the perimeter, in centimeters, of the rectangle?' with provided expressions for the width and length is option a) 2(3.2t + 5.8) + 2(1.8t - 3.8)