Question 1005090
The length of a picture is 4/3 times its width.
It is placed in a picture frame of uniform width of 2cms.
If the area is 100 sq. cms, what are the dimensions of the picture?:
:
let L = the length of the picture
let w = the width of the picture
then because of the 2" uniform width of the frame,
(L+4) = the length including the frame
(W+4) = the width including the frame
;
Assuming they mean the whole area including the frame = 100 sq/cm 
(L+4) * (W+4) = 100
Given that
L = {{{4/3}}}W, replace L
({{{4/3}}}W+4)(W+4) = 100
FOIL
{{{4/3}}}W^2 + {{{16/3}}}W + 4W + 16 = 100 
subtract 100 from both sides
{{{4/3}}}W^2 + {{{16/3}}}W + 4W - 84 = 0 
multiply by 3, get rid of the fraction
4W^2 + 16W + 12W - 252 = 0
4W^2 + 28W - 252 = 0
Simplify, divide by 4
W^2 + 7W - 63 = 0
using the quadratic formula, the positive solution
W = 5.175 cm is the width of the picture
then
L = {{{4/3}}}*5.175
L = 6.9 cm is the length of the picture
:
:
See if the works out
the frame dimensions are 4" longer than the picture
9.175 * 10.9 = 100.0 sq/cm