the length of a rectangle is 3 cm more than the width. the area is 70cm^2. find the dimensions of the rectangle.

Question

The length of a rectangle is 3 cm more than the width. The area is 70cm² . Find the dimensions. 

Answer 1

A=lw  [Generalized equation for area]

l=w+3 [Length is 3 more than the width]

w=w

 

70=(w+3)w [Substitute defined variables into the generalized equation]

70=w²+3w

w²+3w-70=0  [Now solve by quadratic formula, factoring, or completing the square]

(w+10)(w-7)=0

w=-10,7 [Because it is quadratic, there are 2 possible answers, but the width cannot be negative, so -10 is eliminated]

 

Because the width is 7, the length must be 10

 

Answer 2

Hi Victoria,

 

let x = width

 

then x + 3 = lenght

 

A = lw

 

70 = (x+3)(x)

 

70 = x² + 3x

 

0 = x² +3x -70

 

factor

 

0 = (x-7)(x+10)

 

set each factor to 0 and solve for x

 

x-7 =0

x = 7            (the width is 7

 

x+3=10        (the lenght is 10

 

The other factor would give us a negative value for x and we can't have a negative length

 

Hope this helps