Solve by an equation

Question

jill wants to buy a mat for a photograph that is 14cm by 20cm. She wants to have a even border around the picture when it is mounted on the mat. if the area the the mat she chooses is 352cm how wide will the border be?

Answer 1

Let X be the width of the border around the picture.  

 

The border is on all 4 sides (top and bottom, left and right) so the total size of the photograph plus border is 

(14 + 2*X) by (20 + 2*X) 

 

This area is 352 so  

 

(14 + 2*X)*(20 + 2*X) = 352

280 + 40*X + 28*X + 4*X² = 352

4*X² + 68*X - 72 = 0

X² + 17*X - 18 = 0

(X + 18)*(X - 1) = 0  

 

X = -18  or  X = 1  

 

The border cannot have a negative width so discard X = -18  

 

The border will be 1 cm wide  

 

Check:  (14 + 2)*(20 + 2) = 16*22 = 352