Question

perimeter & area of rectangles
click on squares to make a rectangle with an area of 18 square units and a perimeter of 22 units.

Explanation:

Step1: Recall formulas for rectangle

The area of a rectangle is \( A = l \times w \) (where \( l \) is length, \( w \) is width) and perimeter is \( P = 2(l + w) \). We know \( A = 18 \) and \( P = 22 \).

Step2: Solve for length and width

From \( P = 22 \), divide by 2: \( l + w = 11 \). From \( A = 18 \), find pairs of positive integers that multiply to 18: (1,18), (2,9), (3,6). Check which pair adds to 11: \( 2 + 9 = 11 \). So length = 9, width = 2 (or vice versa).

Step3: Identify the rectangle on the grid

On the grid, select a rectangle with 9 units in one side (horizontal) and 2 units in the other (vertical), or 2 units horizontal and 9 units vertical. Count 9 squares along one row and 2 rows (or 2 squares along a row and 9 rows) to make the rectangle with area \( 9\times2 = 18 \) and perimeter \( 2(9 + 2)=22 \).

Answer:

A rectangle with length 9 units and width 2 units (or length 2 units and width 9 units) should be formed by clicking on the corresponding squares in the grid. Specifically, select a 9 - column (or 2 - column) and 2 - row (or 9 - row) arrangement of squares.