# Need some help with Applications and Problem Solving .

Need some help with Aplications and Problem Solving .....

Framing a Photo - A photo measuring 12 cm by 8cm is to be surrounded by a mat before framing. The width of the mat is to be the same on all sides of the photo. The area of tht mat is to equal the area of the photo. Find the width of the mat.

Could anybody show me a sulotion to this problem, im having trouble on this one .... LMK Thx

It needs to be 12 X 8 which has an area of 96 cm. We will call the sides of the frame 'a' and we know that all the sides have a length of 'a'. the area of the area inclosed by the frame is just a*a. So we need to take the total area enclosed (a^2) then subtract the area of the picture inside (12*8) and set equal to the final area that the frame takes up (96cm). 96=a^2 -96
a^2=192
a=192^(1/2)=13.85cm

The width of the mat is (if I read correctly) the width of the border that surrounds the picture.

The problem now becomes:

If I have a photo with area 96 and then put a border around the picture with the same area my total area (photo+border) will become 192.
Now this equals (8+2x)(12+2x), because the photo has the measurement 8*12 and these lengths increase with twice the width of the border (which I call x) which is the same on all four sides. Now if you solve (8+2x)(12+2x) = 192, the answer will be x = 2.