NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 6: Mensuration - Problems and Solutions
Question 53

Question. 53

Perimeter of square and rectangle same. Square side = 15 cm, rectangle one side = 18 cm. Find rectangle area.

Answer:

162 cm²

Detailed Answer with Explanation:

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).

NCERT Exemplar Solutions Class 6 – Mathematics – Unit 6: Mensuration – Problems and Solutions | Detailed Answers