Dimensions of rectangle

Question

The length of a rectangle is 11cm less than twice its width. If the area of the rectangle is 13cm² , find the dimensions of the rectangle

Answer 1

A = lw

l = 2w - 11

13 = (2w - 11)w

13 = 2w² - 11w

2w² - 11w - 13 = 0

(2w - 13)(w + 1) = 0

 

2w - 13 = 0

2w = 13

w = 6.5 cm

 

w + 1 = 0

w = -1

Because length is not negative, this answer is out.

 

l = 2(6.5) - 11

l = 13 - 11

l = 2 cm

 

Or...

 

13 = 6.5l

l = 2 cm

 

Usually the length is the longer portion, but we have a 2 x 6 cm rectangle.

Answer 2

Say the width of the rectangle is x cm so the length will be 2x-11 cm . Now the area will be length x width = (2x-11)x = 2x²-11x cm²

Given that the area is 13 cm².

So, 2x²-11x=13

Or

2x²-11x-13 =0 (factorizing)

2x²-13x+2x-13=0

x(2x-13)+1(2x-13)=0

(2x-13)(x+1)=0

so x= 13/2=6.5 or x = -1

 

width cannot be a negative number so we accept x as 6.5 cm so length is 2x-11 = 13-11=2cm

 

So dimensions are length = 2 cm and width is 6.5 cm