Question

The ratio of the length of two rectangles is 24 : 23 and the breadth of the two rectangles is 18 : 17. If the perimeter of the second rectangle is 160 cm and the length of the second rectangle is 12 cm more than its breadth, then find the area of the first rectangle ?

• A. 1444 sq cm
• B. 1480 sq cm
• C. 1610 sq cm
• D. 1728 sq cm

Answer 1

Answer:

D. 1728 sq cm

Solution: Calculation: Perimeter of second rectangle is 160 cm ⇒ 2( L2 + B2 ) = 160 ⇒ ( L2 + B2) = 80cm ------ eq1 And one more relation of length and breadth is ⇒( L2 - B2 ) = 12 cm ------ eq 2 Add Eq 1 and eq 2 we get ⇒ 2L2 = 92 → L2 = 46 cm ⇒ B2 = 46 -12 = 34 cm Then Ratio of L1 and L2 is 24 : 23 ⇒ 23 unit = 46 cm ⇒ 24 unit = 48 cm Ratio of breadth is 18 : 17 ⇒ 17 unit = 34 cm ⇒ 18 unit = 36 cm Then length of L1 is 48 cm and Breadth of B1 is 36 Area of rectangle is 48 × 36 ⇒ 1728 sq cm Hence 1728 sq cm is the correct answer.