SOLUTION: A picture is framed on colored cardboard 40 cm by 32 cm. If there is a uniform boarder around the picture such that the area of the boarder is 720 cm^2, find the dimensions of t
Algebra.Com
Question 90942: A picture is framed on colored cardboard 40 cm by 32 cm. If there is a uniform boarder around the picture such that the area of the boarder is 720 cm^2, find 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 framed on colored cardboard 40 cm by 32 cm. If there is a uniform boarder around the picture such that the area of the boarder is 720 cm^2, find the dimensions of the picture.
:
Draw a rough diagram of this; label the outer dimension of the frame as 40
by 32.
Label the width of the border as x. It will be apparent that the dimensions
of the picture will be (40-2x) by (32-2x)
:
If we find the width of the border it will be easy to find the dimensions of the picture:
:
Find the area of the colored cardboard: 40 * 32 = 1280 sq/cm
Overall area: 1280
Border area: -720
-------------------subtract
Picture area: 560 sq/cm
:
A simple area of the picture equation:
(40-2x)(32-2x) = 560
FOIL
1280 - 144x + 4x^2 = 560
:
Arrange as a quadratic equation:
4x^2 - 144x + 1280 - 560 = 0
4x^2 - 144x + 720 = 0
:
Simplify, divide by 4:
x^2 - 36x + 180 = 0
:
Factors to:
(x-6)(x-30) = 0
:
x = +6
and
x = +30
:
Obviously the smaller value is our solution, x = 6
The dimension of the Picture:
40 - 2(6) = 28
32 - 2(6) = 20
;
Check our solution by finding the area
28 * 20 = 560
:
Did this makes sense? Any questions?
RELATED QUESTIONS
a picture frame on colored cardboard 40 cm by 32cm. if there is a uniform border around... (answered by greenestamps)
a picture frame on colored cardboard 40 cm by 32cm. if there is a uniform border around... (answered by Boreal)
a picture frame is 26 cm. by 18 cm. It is pasted on a colored cardboard so that there is... (answered by mananth)
a picture frame is 26 cm. by 18 cm. It is pasted on a colored cardboard so that there is... (answered by mananth)
a framed picture has lenght 35 cm and width 25 cm. the picture itself has area 375 cm.... (answered by nerdybill)
a framed picture has length 35 cm and width 25 cm. the picture itself has area 375 sq cm. (answered by jonvaliente,checkley75)
The frame on a picture is 28 cm by 32 cm outside and is of uniform width. What is the... (answered by lwsshak3)
A picture 18 cm by 15 cm, has a uniform frame around it. If the area of the frame is 234... (answered by lwsshak3)
a 40 cm square handkerchief has a boarder 4 cm wide around it. what is the area of the... (answered by richwmiller)