Question

a rectangle is divided into four small rectangles as shown. the perimeters of three of the four small rectangles are $24$, $32$, and $42$, respectively. the remaining small rectangle has the shortest perimeter among the four. what is the perimeter of the remaining rectangle?

Answer 1

The perimeter of the remaining rectangle is $0.

Step-by-step explanation:

The perimeter of a rectangle is the sum of the lengths of all its sides. In this question, we are given that the perimeters of three of the four small rectangles are $24, $32, and $42. Let's assume the perimeters of the four small rectangles are P1, P2, P3, and P4 respectively. Also, let's assume that P4 is the perimeter of the remaining rectangle.

We are given P1 = $24, P2 = $32, and P3 = $42. To find P4, we need to subtract the perimeters of three small rectangles from the total perimeter of the larger rectangle. The total perimeter of the larger rectangle is the sum of the perimeters of all four small rectangles.

Therefore, P4 = (P1 + P2 + P3 + P4) - (P1 + P2 + P3).

Substituting the given values, we get P4 = ($24 + $32 + $42 + P4) - ($24 + $32 + $42).

Simplifying the equation, we have P4 = $98 - $98 = $0.

Therefore, the perimeter of the remaining rectangle is $0.