A rectangle has length three times its breadth. If its perimeter is $48, cm$ , which is greater: the area of the rectangle or the area of a square with side $6, cm$ ?

hard 4 marks Class 7 · Mathematics · Comparing Quantities

Answer

The area of the rectangle is greater.

The correct answer is The area of the rectangle is greater. — Step 6: Compare the two areas: $108 > 36$ , so the rectangle’s area is greater.

Step-by-step solution

Step 1: Let the breadth be $b$ cm. Then the length is $3 b$ cm.
Step 2: Use the perimeter formula $2 (l + b) = 48$ to find $b$ . $2 (3 b + b) = 48 R i g h t a r r o w 2 (4 b) = 48 R i g h t a r r o w 8 b = 48 R i g h t a r r o w b = 6$ cm.
Step 3: Compute the length: $l = 3 b = 18$ cm.
Step 4: Find the area of the rectangle: $A_{rect} = l \times b = 18 \times 6 = 108, cm^{2}$ .
Step 5: The area of the square with side $6$ cm is $A_{sq} = 6^{2} = 36, cm^{2}$ .
Step 6: Compare the two areas: $108 > 36$ , so the rectangle’s area is greater.

Common mistake: Assuming a longer side automatically gives a larger area without computing the actual area.

Concept tested: Area comparison of rectangle and square