David V.

asked • 04/18/16

A picture is 4cm by 6cm. it is pasted onto a matte of equal width on all sides. find the width of the matte if the area of the matte is 3 times as greater

we have been using the quadratic formula and completing the square in math. the question is : A picture is 4cm by 6cm. it is pasted onto a matte of equal width on all sides. find the width of the matte if the area of the matte is 3 times as great as the area of the picture

1 Expert Answer

By:

Mark M. answered • 04/18/16

Tutor
5.0 (278)

Mathematics Teacher - NCLB Highly Qualified

See tutors like this
See tutors like this
First the area of the matte
(4 + 2w)(6 + 2w)
24 + 12w + 8w + 4w2
4w2 + 20w + 24
This is three times the area (24) of the picture
4w2 + 20w + 24 = 3(24)
4w2 + 20w - 48 = 0
w2 + 5w - 12 = 0
w2 + 5w + (5/2)2 = 12 + (5/2)2
(w + 2.5)2 = 73/4
w + 2.5 = ±√73 / 2
w = -2.5 ±√73 / 2
 
The width is -2.5 + √73 / 2, or approximately 1.772 cm
 
Upvote • 0 Downvote
More
Report

David V.

When i divided 48 by 4 i got 12 not 21, was that a mistake or am in not getting what you did there?
Report

04/18/16

Mark M.

That's my error, thank you for commenting. I shall revise.
Report

04/18/16

David V.

sorry im not getting what you're doing here, i see that you do quadratic form half way through but i doesnt seem to be what we have been doing in class, sorry to bother you again and thanks for the help!
w2 + 5w + (5/2)2 = 12 + (5/2)2
(w + 2.5)2 = 73/4
w + 2.5 = ±√73 / 2
w = -2.5 ±√73 / 2
 
Report

04/18/16

Mark M.

You are welcome. No bother!
You say you have been "completing the square." That is the process that I used.
(5/2) = one-half of the linear coefficient. The square of that is added to both sides.
The expression on the left is a perfect square trinomial.
OK?
Report

04/18/16

David V.

Would i be able to plug in 4w2 + 20w - 48 = 0 into the quadratic formula -b±√b2-4(a)(c)/2(a) to get the same answer?
 
Report

04/18/16

David V.

Apparently i'm suppose to use quadratic formula for this question, and only use completing the square for questions that ask for minimum or maximum, could you help me do this question by using -b±√b2-4(a)(c)/2(a). The b2 is b squared by the way, thank you.
Report

04/18/16

David V.

Sorry when i said would i be able to plug in "4w2 + 20w - 48 = 0" i mean't x2+5x-12=0. sorry
Report

04/18/16

Mark M.

w = [-b ± √(b2 - 4ac)] / 2a
w = [-5 ± √(25 - 4(1)(-12))] / 2(1)
Can you do the calculations?
Report

04/18/16

David V.

i got -5±√(73)/2, do i plug it into the calculator as -5-√(73)/2 and -5+√(73)/2 or do i square root 73 first then do -5-8.54/2 and -5+8.54/2. This should be my last question, thanks for all the help!
Report

04/18/16

Mark M.

The part after the "or."
-5 - 8.54/2 is a solution yet does not answer the question - width is positive
-5 + 8.54/2 is the solution that is the width.
You are welcome! Glad to have helped.
Report

04/18/16

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.