An airplane ticket has an area of 119 square centimeters. Its perimeter is 48 centimeters. What are the dimensions of the ticket?

17cm ×7cm

Step-by-step explanation:

Assuming that the airplane ticket is a rectangle,

let the length and the breadth of the ticket be L cm and B cm respectively.

LB= 119 (1)

2(L +B)= 48

L +B= 48 ÷2

L +B= 24 (2)

From (2):

L= 24 -B (3)

Substitute (3) into (1):

B(24 -B)= 119

24B -B²= 119 (expand)

B² -24B +119= 0

(B -17)(B -7)= 0 (factorise)

B -17= 0 or B -7= 0

B= 17 or B= 7

Substitute the values of B into (3):

L= 24 -17 or L= 24 -7

L= 7 or L= 17

∴ The dimensions of the airplane ticket is 17cm ×7cm.