SOLUTION: a picture is 4 inches longer then wide. it a 1 inch frame is put on and the area is increased by 48 square inches. whats the dimensions of the picture

Question 211987: a picture is 4 inches longer then wide. it a 1 inch frame is put on and the area is increased by 48 square inches. whats the dimensions of the picture
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
"a picture is 4 inches longer than it's wide."
:
Let x = the width of the picture
then
(x+4) = the length
:
"if a 1 inch frame is put on, the area is increased by 48 square inches."
(x+4)+ 2 =
(x+6) = overall length
and
(x+2) = overall width
:
"what's the dimensions of the picture"
:
Overall area - picture area = 48 sq/in
:
(x+6)(x+2) - x(x+4) = 48
FOIL
x^2 + 2x + 6x + 12 - (x^2 + 4x) = 48
x^2 + 8x + 12 - x^2 - 4x = 48
x^2 - x^2 + 8x - 4x = 48 - 12
4x = 36
x =
x = 9 in is width of the picture
and
9 + 4 = 13 in is the length
;
:
Check solution:
15*11 - 13*9 =
165 - 117 = 48
RELATED QUESTIONS
a picture is 1 inch longer than it is wide. It is put into a frame 1/2 inch wide. If the... (answered by stanbon)

I can not use algebra. I painted a picture that is 4 inches longer than it is wide. If (answered by josgarithmetic)

a picture is 1 inch longer than it is wide. it is put into a frame one half inch wider on (answered by ankor@dixie-net.com)

A square photograph measuring 8 inches by 8 inches is positioned within a 1 inch wide... (answered by macston)

A rectangular picture is 6 cm longer than it is wide. A wide frame 1 cm wide is placed... (answered by lynnlo)

A Frame 2 inches wide is placed around a rectangular picture with dimensions 8 inches by... (answered by Alan3354)

A frame for a picture is 2.5 inches wide. The picture enclosed by the frame is 5 inches... (answered by fractalier)

A rectangular picture is 3 inches longer than it is wide. It has a frame 2 inches wide... (answered by mananth)

A picture frame holds an 8-inch by 10-inch photograph. The frame adds a border x inches... (answered by MowMow,ikleyn)