a frame painting has an overall dimension of 32" x 29"

area of painting alone is 550 square inches. what is the width of frame??

Guest Nov 27, 2018

#2**+2 **

Square area of the whole framed picture = 32 x 29 = 928 in^2

928-550 = 378 in^2 = area of frame

32 x 29 -( (32-x) (29-x)) = area of frame= 378 in^2 where x = 2 times the width of the frame

928 - x^2 + 61x - 928 = 378

-x^2+61x-378 = 0 Use Quadratic Formula to find x = 54 or 7 (54 is too big...toss it out)

x = 7 width = 1/2 x = 3.5 inches

As a check....does the inside dimension of the frame = the picture size of 550 in^2 ?

(32-7)(29-7) = 550 Check!

ElectricPavlov
Nov 27, 2018

#1

#2**+2 **

Best Answer

Square area of the whole framed picture = 32 x 29 = 928 in^2

928-550 = 378 in^2 = area of frame

32 x 29 -( (32-x) (29-x)) = area of frame= 378 in^2 where x = 2 times the width of the frame

928 - x^2 + 61x - 928 = 378

-x^2+61x-378 = 0 Use Quadratic Formula to find x = 54 or 7 (54 is too big...toss it out)

x = 7 width = 1/2 x = 3.5 inches

As a check....does the inside dimension of the frame = the picture size of 550 in^2 ?

(32-7)(29-7) = 550 Check!

ElectricPavlov
Nov 27, 2018