Can you help me?

Question

A painting is 6 cm longer than it is wide. the painting is to be surrounded by a mat that is 2 cm wide and covered by a piece of glass with area 352 cm squared. find the dimensions of the painting. can you help me?

Answer 1

Let's say x=width, y=length
Since length is 6cm longer than width: y=x+6
The area of the painting is therefore: xy
The mat is 2cm wide surrounding the painting, so the dimensions are increased by 4cm each
The mat is covered by a piece of glass that is: 352cm squared
Since the area of the glass equals the area of the mat + the area of the painting, we have: (x+4)(y+4) = 352
Substituting for y, we get: (x+4)(x+6+4) = 352
Which when multiplied out and simplified, becomes:
x*2 +14x - 312 = 0
Factored, this gives us: (x+26)(x-12)=0
For this equation, if either term equals 0 then the equation holds true, therefore: x = -26 or +12
Since -26 doesn't make sense for a measurement, then x must equal +12
So the dimensions of the painting are: x=12 and y=12+6=18

Answer 2

"A painting is 6 cm longer than it is wide."

l - 6 = w

"the painting is to be surrounded by a mat that is 2 cm wide"

(so the length and width will each be increased by 4cm)

"and covered by a piece of glass with area 352 cm squared."

(l + 4)(w + 4) = 352

Can you solve it from there?

Answer 3

Let w = width of painting. Then w + 6 = length of painting. The width of the matte is w + 4, and the length of the matte is w + 10. This allows 2cm of matte on all four sides. The glass must cover the entire mounting and is 352 sq cm in area. So (w+4)(w+10) = 352.

Answer 4

x = lenght of painting
y = width of painting

x = y + 6 ----> (6 cms longer than wide)

(x + 2)*(y + 2) = 352 (the width of the mat multiplied by the length of the mat equals the area of glass)

Solving these two equations will give you y=14, x=20

Therefore the painting is 14 cms wide and 20 cms long.