problem-solving find unknown length

Question

The painting is on a piece of canvas that has an area of the hundred and 80 in.². The length of the painting is 1 1/4 times the width. What are the dimensions of the painting?

Answer 1

Andrea,

 

Area=length*width

 

180=5/4w(w)  [The length is 1 /4, or 5/4 times the width]

180=5/4w²

180(4/5)=w²   [Remember when dividing by a fraction, you multiply by its reciprocal]

720/5=w²

144=w²

±12=w           [Since the width can't be negative, we can eliminate the negative possibility]

w=12

 

180=L(12)    [Substitute the value of w and solve for L]

15=L

 

The dimensions are 12x15

 

I hope this helps.

Answer 2

area of the hundred??  This is what I think you meant.  

 

Area of a canvas(rectangle) = length * width

 

length = 1.25*width

 

substitute.  80= 1.25w * w 

 

80 = 1.25w^2  Divide both sides by 1.25

64 = w^2  Take the square root

8 inches= width

So therefore l = 1.25(8)

length = 10 inches