Perimeter of square and rectangle same. Square side = 15 cm, rectangle one side = 18 cm. Find rectangle area.
Step 1: Perimeter of the square
Perimeter of a square = (4 imes ext{side})
(4 imes 15 = 60 ext{cm})
Step 2: Perimeter of the rectangle
Given: Both perimeters are the same, so rectangle perimeter = (60 ext{cm}).
Step 3: Let the rectangle sides be
Length (= 18 ext{cm}), breadth (= b ext{cm})
Perimeter of a rectangle (= 2 imes ( ext{length} + ext{breadth}))
(2 imes (18 + b) = 60)
Step 4: Solve for (b)
Divide both sides by 2: (18 + b = 30)
Subtract 18 from both sides: (b = 12 ext{cm})
Step 5: Find the area
Area (= ext{length} imes ext{breadth})
(= 18 imes 12)
(= 216 ext{cm}^2)
Note: The earlier line “Area = (18 imes 9)” (giving (162 ext{cm}^2)) was a typo. With perimeter (60 ext{cm}), the breadth must be (12 ext{cm}), so the correct area is (216 ext{cm}^2).