Question 1
The vertices of two rectangles are A(−5,−1),B(−1,−1),C(−1,−4),D(−5,−4) and W(1,6),X(7,6),Y(7,−2),Z(1,−2). Compare the perimeters and the areas of the rectangles. Are the rectangles similar? Explain.

Answer:

yes

Step-by-step explanation:

The perimeter of the rectangle ABCD and WXYZ are 14 units and 28 units respectively. The perimeter of the rectangle ABCD and WXYZ are 12 units² and 48 units² respectively.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The perimeter of a rectangle = 2(L+W)

The vertices of two rectangles are A(−5,−1),B(−1,−1),C(−1,−4),D(−5,−4) and W(1,6),X(7,6),Y(7,−2),Z(1,−2).

As per the given data, the figure of two rectangles has been attached below.

According to the graph,

The perimeter of the rectangle ABCD = 2(3 + 4) = 2(7) = 14 units

The perimeter of the rectangle WXYZ = 2(6 + 8) = 2(14) = 28 units

The area of the rectangle ABCD = (3 × 4) = 12 units²

The area of the rectangle WXYZ = (6 × 8) = 48 units²

The rectangles are similar because the ratio of length to width is equivalent.

The perimeter of the rectangle ABCD and WXYZ are 14 units and 28 units respectively. The perimeter of the rectangle ABCD and WXYZ are 12 units² and 48 units² respectively.

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