Find the width

Question

The outside dimensions of a picture frame are 28cm by 23 cm. The area of the picture is 414 square centimeters. Find the width of the frame itself. 

 

A). Give the answer for the width of the picture frame. 

Answer 1

w=width of picture frame

the length of the picture is 28-w-w=28-2w

the width of the picture is 23-w-w=23-2w

A=lw

414=(28-2w)(23-2w)

414=644-46w-56w+4w²

0=644-414-102w+4w²

4w²-102w+230=0

divide both sides by 2

2w²-51w+115=0

factor

2*115=2*5*23 and (2*23)+5=46+5=51, the coefficient of the middle term

(2x-5)(x-23)=0

2w-5=0

2w=5

w=5/2=2.5 cm

the width of the frame is 2.5 cm

check:the picture itself has dimensions 28-2.5-2.5=28-5=23 cm and 23-2.5-2.5=23-5=18 cm

23*18=414 sq cm, the area of the picture itself