Word Problems

Question

The perimeter of a rectangle is 62m. Find the length of its sides if it is known that the area of the rectangle is 1980000 cm².

The perimeter of a rectangle is 62m. Find the length of its sides if it is known that the area of the rectangle is 1980000 cm².

Answer 1

Perimeter = 2(length + width)

2(L + w) = 62

L + w = 31  {equation 1}

 

Area = Length*Width

LW = 1980000 cm²

Note our perimeter is in meters and our

area is given in square centimeters.  Since

there are 100cm per meter, divide the

1980000 cm² by 100² or 10,000 to change

it to square meters.

 

LW = 198 m²  {equation 2}

 

From equation 1, W = 31- L

Substitute that into equation 2

 

L(31-L) = 198

31L - L² = 198

 

Get all terms to same side to

create a quadratic

 

L² - 31L + 198 = 0

From quadratic equation with

a=1, b =-31, c = 198

 

L = [31±√((-31)²-4(1)(198))]/2(1)

L = (31 ±√169)/2

L = (31 ± 13)/2

 

L = 44/2 = 22

L = 18/2 = 9

 

The rectangle is 22m by 9m

 

Area:

22m = 2200cm

9m = 900cm

(2200)(900) = 1,980,000 cm²