Question 1186662: a picture frame on colored cardboard 40 cm by 32cm. if there is a uniform border around the picture such that area of the border is 720 cm2.find the length and width of the picture
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! It helps to draw this.
The picture is (40-2x) by (32-2x), where x is the width of the border, assuming the picture is centered.
That area is 1280-144x+4x^2 cm^2 for the picture
the whole frame is 1280 cm^2 (40cm x 32 cm)
the border is the area of all-the picture area=720 cm^2
so 1280-(1280-144x+4x^2)=720
so -4x^2+144x-720=0
4x^2-144x+720=0
x^2-36x+180=0
(x-30)(x-6)=0
x=30 and 6 cm. Only the 6 cm makes sense; the 30 cm is extraneous.
The border is 6 cm.
The picture has dimensions 28 cm x 20 cm, which is the answer.
That makes the picture area 560 cm^2, the border area 720 cm^2, which adds to 1280 cm^2.
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