Question

The width of a rectangle is 3 less than its length. If the length is multiplied by 2 and the width is increased by 4, the perimeter of the new rectangle is 80. What are the dimensions of the new rectangle?

A) Length = 11 units, Width = 8 units
B) Length = 14 units, Width = 11 units
C) Length = 17 units, Width = 14 units
D) Length = 20 units, Width = 17 units
E) Length = 23 units, Width = 20 units

Answer 1

The dimensions of the new rectangle are "D) Length = 20 units and Width = 17 units".

Step-by-step explanation:

Let's denote the length of the original rectangle as L and its width as W. According to the given information, we have the relationship: (W = L - 3). The perimeter of a rectangle is given by (2L + 2W). Therefore, the perimeter of the original rectangle is (2L + 2(L - 3)).

Now, the problem states that if the length is multiplied by 2 (2L) and the width is increased by 4 (W + 4), the new perimeter is 80. So, the equation becomes (2(2L) + 2(W + 4) = 80).

Solving these equations simultaneously will give us the values of L and W. After finding the values, we get "Length = 20 units and Width = 17 units, matching option D".

In conclusion, the dimensions of the new rectangle are Length = 20 units and Width = 17 units, as determined by solving the system of equations derived from the given conditions.