The area of a bookmark is 140 square centimeters. The perimeter is 54 centimeters. What are the dimensions of the bookmark?

See explanation

Step-by-step explanation:

Recall that all the sides of the square are equal

Hence;

Area of a rectangle= l * b equation 1

Perimeter of a rectangle = 2(l + b)equation 2

Area of the rectangle = 140 square centimeters

140 = lb

l = 140/b

Perimeter of the rectangle =  54 centimeters

substituting l = 140/b into equation 2

54 = 2(140/b + b)

Multiplying through by b

54b = 280 + 2b^2

Hence;

2b^2 - 54b + 280 = 0

Solving the quadratic equation

b=20 or b=7

substituting b=20 or b=7 into l = 140/b

l = 140/20 or l = 140/7

l = 7 or 20

THEREFORE;

b=20 cm or b=7 cm

l = 7cm or 20cm

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step-by-step explanation: