Math Problem Need Help? Thank You?

Question

I have a quadratic word problem. Its asking ( a photographer wants to frame a print with a matte of uniform width all around the print. To make it pleasing to the eye the area of the matte should equal the area of the print. If the print measures 40cm by 60cm how wide should the matte be?) Can someone show me how to do it. Help would be apreciated. Thank You!!

Answer 1

LW = 2*2400 = 4800 cm^2
(2w + 60)(2w + 40) = 4800
(w + 30)(w + 20) = 1200
w^2 + 50w + 600 = 1200
w^2 + 50w + 625 = 600 + 625
(w + 25)^2 = 1225
w + 25 = 35
w = 10 cm

Answer 2

Let the width of matte = w cm

Then the size of the finished framed photo would be 40+2w cm by 60+2w cm

Area of framed photo = 2* Area of print ( since area of matte = are of print)

(40+2w)(60+2w)=2*40*60= 4800
This reduces to

w^2+50w-600=0

On solving this quadratic eqn, you will get the value of w = 10 cm

The width of the matte should be 10 cm.

Answer 3

Print measures 40cm by 60cm.
So the area of the print will be 40 * 60 = 2400
Let the width of matte be x cm.
this is sure the total length of matte is equal to the perimeter of the print, that is (60 +40 +60 +40) = 200cm.
since the area of print is equal to the area of matte,
so 200 * x = 2400
on simplifying, x = 2400 / 200
or x = 12
So the width of matte should be 12cm.

Answer 4

Draw the picture... 2 rectangles, one smaller within the other.
Now label the sides. Inside you have 60 high and 40 wide.

the outside is defined by the inside plus the variable y. The area =2400 right.

So define the area of the matte using the inside dimensions and y.

2{(60+2y)*y} + 2(40*y)=2400

Solve the quadratic equation for y.

Answer 5

The area of the print = 240 cm
The area of the mat must also be 240.
Therefore the area of the mat before the print area is removed must be 480.
The mat must measure 60cm by 80cm