Question

A framed picture has length 50 cm and width 40 cm . The picture itself has area 1344 cm^2. How far is it from the edge of the picture to the edge of the frame if thid didtance is uniform around the picture ?

Answer 1

if the width of the frame is w, the dimensions of the picture are 50-2w and 40-2w (subtract w on each side). So, since we know the area of the picture,

(50-2w)(40-2w) = 1344
w = 4

Check:
picture area is 32x42 = 1344

Answer 2

1325

Answer 3

To add on to Steve's answer ( No guess and check )
(50-2x)(40-2x) = 1344
4x^2 -180x +2000 = 1344
4x^2 -180x +656=0
Then we will use the Quadratic Formula
180 ± √32,400 - 10496 / 8
-180 ± 148 / 8
4 or 41. We can not use 41 as it will be two big. If u substitute 4 instead of x in the original equation.
50 - 2(4) * 40 - 2(4)
50 - 8 * 40 * 8
So the width of the frame is 8 Centameters

Answer 4

Let m be the width of the frame. Then:
(50-2m)(40-2m)=1344
2000-180m+4m²=1344
4m²-180m+656=0
m²-45m+164=0
(m-41)(m-4)=0
m=41 or 4
The frame is 4 inches wide ....................