13 A picture has a width of 8cm and length of 14 cm If the p

13. A picture has a width of 8cm and length of 14 cm. If the perimeter of the picture is increased by 50 percent, which of the following dimensions is possible for the new perimeter?

A. 16cm by 28cm

B. 8cm by 28cm

C. 4cm by 7cm

D. 12cm by 21cm

Solution

We know that the perimeter of a rectangle is 2 ( breadth + length). Here, the perimeter of the picture = 2 ( 8 + 14) = 2 (22)   = 44 cm. Now, if the perimeter of the picture is oncreased by 50 %, then the new perimeter = 44* 150 % = 66cm. If the new breadth and the lenght are b and l cm respectively, then 2 (b + l) = 66 or, b + l = 33.Of the given 4 options, the only correct option is D as 12 + 21 = 33. In all other options, the breadth + lenght is not equal to 33 cm.Thus, the correct answer is D i.e. 12 cm by 21 cm.