the width of a rectangle is 2 inches less than its length, and the area is 35 square inches. what is the length and width?

Question

I need help with this word problem. It's crunch time.

Answer 1

Hi Sarah,

 

Ok

 

let Length = x

 

then width = x -2  (2 inches less than length

 

now

 

A = Lw

 

35 = x (x -2)

 

35 = x² - 2x

 

x² -2x -35 = 0

 

(x-7)(x+5) = 0  

 

x-7=0

 

x=7       (we won't use the other factor since it would give us a negative length

 

so length = 7

 

width = 7 -2 = 5

 

Hope this helps

Answer 2

Hi,

 

Here you have to make sure you interpret the problem correctly. 

 

There is Width and Length of a rectangle, and the width is 2 inches less than the length of a rectangle. This implies that you can assign an unknown letter, X, to be the length and hence the width will be (X-2) which is exactly what's stated in the problem.. 

 

Using the formula for the area of rectangle, Area= (width)*(length), in this case Area = (X-2)*(X), since its area is given and it is 35 square inches, helps you to find the unknown 

 

This leads you to solving the equation (X-2)(X)=35 => X²-2X-35=0... This is a quadratic expression that may have to real values, after solving, keep the one that makes sense. 

Answer 3

length = l

width = "width is" means w = "2 inches less" means subtract 2 "than" [switch first and last] "its length" means l= l - 2

Area = 35 in 2

Area of a rectangle = (l)(w)

Substitute

A = (l)(l-2)
35 = (l)(l-2)

Distribute/Multiply

35 = l2 - 2l

Balance
l2 - 2l - 35 = 0

Factor

(l - 7)(l + 5) = 0

Solve (set each factor = to 0)

This will lead you to find the length

Re-read question to find the phrase that will help you find the width

Answer 4

Let X = the length; then the width = X - 2

the Area of a rectangle = L x W = X(X - 2)

since the area = 35cm², we write 35cm² = X(X - 2)

expanding this equation, 35cm2 = X2 - 2X

rewriting, 0 = X2 - 2X -35cm²

factoring, 0 = (X - 5cm)(X + 7cm)

so the two roots are -5 and +7, but since no length can equal a minus number, we can discard that root

which leaves us with +7cm, thus X - 2 = +5cm

so, the length = +7cm, and the width = +5cm