the width of a rectangular picture is 9 in. less than the length. the erae of the picture is 70 in

Question

70in²

 

Answer 1

l=length

l-9=width

A=l*w

70=l*(l-9)

70=l^2-9l

l^2-9l-70=0

(l-14)(l+5)=0

l-14=0

l=14 inches

l-9=5 inches

length=14 inches

width=5 inches

without algebra...

70=2*5*7=(2*7)*(5)=14*5 and 5 is 9 less than 14

Answer 2

Hi Kim

 

Let's say

L = length

W = width

W = L-9

We know that A = LW

A = 70

 

Using substitution we can write area as

 

L(L-9) = 70

 

L² - 9L = 70

and

L² - 9L - 70 = 0

 

We now have a quadratic equation which we can factor

(L-14)(L+5) = 0

L-14 = 0       L+5 = 0

L = 14           L = -5

 

We through out the 2nd solution (L=5) since a length cannot be negative

L = 14

W = L-9 = 14-9 = 5