Question

You plotted a rectangle ABCD on Graph 1 and your friend plotted a square PQRS on Graph 2. Which of the following options is incorrect?

• A. The perimeter of the rectangle ABCD is greater than the square PQRS.
• B. The perimeter of the square PQRS is greater than the perimeter of the rectangle ABCD.
• C. The side AD of the rectangle ABCD is equal to the side PS of the square PQRS
• D. The side PQ of the square PQRS is greater than the side AB of the rectangle ABCD.

Answer 1

The correct option is A The perimeter of the rectangle ABCD is greater than the square PQRS.

The coordinates of the square PQRS are P(−5, 8), Q(1, 8), R(1, 2), and S(−5, 2).
As PQRS is square, all of its 4 sides must be equal.
Side of the square = Side of the figure PQ = Side QR of the figure = Side RS of the figure = Side PS of the figure

Coordinates		Distance
P(−5, 8) and Q(1, 8)	y-coordinates are the same for both the points; the absolute value of the difference of x-coordinates will give the length PQ	Length = |−5 − 1| = |−6| = 6 units

Length of each side of the square, PQRS, is 6 units.
PQ = QR = RS = PS = 6 units
Perimeter of the square PQRS $=4\times$ side of the square
$=4\times 6$
$=24$ units
The coordinates of the rectangle ABCD are A(2, 4), B(7, 4), C(7, −2), and D(5, −2)
Length of the rectangle = Side AB of the figure
Width of the rectangle = Side BC of the figure

Coordinates		Distance
A(2, 4) and B(7, 4)	y-coordinates are the same for both the points; the absolute value of the difference of x-coordinates will give the length AB.	Length = |2 − 7| = |−5| = 5 units
B(7, 4) and C(7, −2)	x-coordinates are the same for both the points; the absolute value of the difference of y-coordinates will give the length BC.	Length = |4 − (−2)| = |4 + 2| = 6 units

Side AB = side CD = 5 units
Side BC = side AD = 6 units
Perimeter of the rectangle $=2\times$ (length + width)
$=2\times (5+6)$
$=22$ units

The side PQ of the square PQRS (6 units) is greater than the side AB of the rectangle ABCD (5 units).
Option A is correct.

The perimeter of the rectangle ABCD (22 units) is smaller than the square PQRS (24 units).
Option B is incorrect, and option D is correct.

The side AD of the rectangle ABCD (6 units) is equal to the side PS of the square PQRS (6 units).
Option C is correct