Question 1207821
An artist has 50 inches of oak trim to frame a painting. The frame is to have a border 3 inches wide surrounding the painting. 

(a) If the painting is square, what are its dimensions? What are the dimensions of the frame? 

(b) If the painting is rectangular with a length twice its width, what are the dimensions of the painting? What are the dimensions of the frame?

An artist has 50 inches of oak trim to frame a painting. The frame is to have a border 3 inches wide surrounding the painting. 

Let the side of the painting be x inches
There is a border of 3 inches all round.

length of the side of frame will be (x+6)   ( 3 in on either side.)

Perimeter is 50 inches

4(x+6) =50   ( 4 sides)

4x+24 =50
4x= 26
x= 6.5 inches
Painting is a square with side 6.5 inches and frame with 12.5 inches side

(b) If the painting is rectangular with a length twice its width, what are the dimensions of the painting? What are the dimensions of the frame?

Let width  of painting  be x in. the  length will be 2x
frame dimensions 
x+6 and 2x+6

perimeter 

2(x+6)+2(2x+6)=50 

2x+12 +4x+12=50
6x = 26
x= 4.33   with
Length = 2x= 8.66 in
Add 6 to both sides to get the frame dimensions

 The dimensions of the framed painting are  10.33 inches by 14.67 inches.