Mark C. answered • 09/23/15
Tutor
New to Wyzant
Former Space Shuttle Engineer w/ Teaching Background
Hi I'm Mark
I am an Electrical Engineer (who used to work on the Space Shuttle - I will help you with this, but you will still need to do some work too!)
Break the question into chunks so you can see what info your given.
1.) "A picture frame has a total perimeter of 3 feet."
You must INFER that "a picture frame" is either a Square or a Rectangle - given what is said next - its a rectangle in this case.
NOW: On your paper, RE-WRITE the Problem and DRAW a Rectangle.
If you do not know what "total perimeter" means - then you must look up the word and memorize it. Sometimes the problem is with your vocabulary knowledge more than your math knowledge. Total Perimeter means the total length of all outside edges added together (like the circumference of a circle - but for a rectangle). Look it up if this is not clear to you.
What is the GENERIC Formula for the Perimeter of a Rectangle in terms of Length and Width? YOU MUST LOOK THIS UP and REMEMBER IT if you do not know...
Assign each side a Letter so that you can build two formulas: W (width) L (length) - NOTE: WHY do you NEED two formulas??? Width is shorter than Length so label the left and right side of your Rectangle drawing with a W, and the Top and the Bottom of it each with a L.
Also while we are at it we can assign P as (Perimeter) - we are told that P = 3 ft.
So now use your knowledge of the Perimeter of a Rectangle to write your first equation:
P = ??? YOU will need to tell ME what P is in terms of W and L.
and you already know that P = 3 ft so you can write ??? = 3 ft. once you figure that out.
2.) "The width of the frame is 0.62 times its length."
More evidence this is a rectangle (and that the "width" is the short side, the "length" the long side.)
Now you need to understand how to translate WORDS into MATH. "is" means equals and "times" means MULTIPLY, so rewrite this sentence. I will use parentheses to indicate multiplication a(b) - pls let me know if you do not understand what this means. Other forms are 1) the 3rd Grade form: a x b or 2) the other algebra form a.b
So we can write:
The width of the frame = 0.62 (its length)
now plug in your letters to get your second equation...
W = 0.62(L)
3.) "Find the dimensions of the frame." What is this asking for? Note that dimensionS is PLURAL...
You should easily SEE that the question is asking for TWO answers - The numerical Values for L (length) and W (width).
You should also notice that the question IMPLIED a level of significant figures by giving you a width/length ratio of 0.62 - that is expressed to the nearest 1/100th (two decimal places past the Zero). Your answers should also be expressed to the same level of significance. (Give the answers out to two decimal places.)
Now, since you need to find Two Unknowns, you need to have two Equations, and you do.
YOU SOLVE THIS BY SUBSTITUTION
Once you write the Equation for P (Perimeter) = (???) in terms of L and W you can SUBSTITUTE things into it that you now KNOW are true.
Re-write your Perimeter Equation and 1) substitute 3 ft in for the P 2) substitute 0.62(L) in for the W
You will now have an equation total in terms of L - SOLVE IT for L
Go ahead... I will wait... :)
Now, Take THAT answer and substitute it into the W = 0.62(L) in place of the letter L.
Multiply that out and get W. Round your answer appropriately.
4.) CHECK YOUR ANSWERS: Round your answers and plug them back into the perimeter equation to check your work.
5.) NEATNESS COUNTS so you can FIND ANY MISTAKES AND FIX THEM !!!
Your MATH and answers MUST flow down your page underneath your drawing.
If you do not lay our your problem and answer on the page fully in a mathematical way I would take off points.
Just slopping some numbers on your page IS NOT ALGEBRA and it IS NOT MATHEMATICS
When your done, you can look below, but NOT until you have TRIED this problem.
Hint: there are 2 L's and 2 W's in the Perimeter of a Rectangle !!!
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Now if you want to CHEAT YOURSELF - look below. OR save the following to CHECK your Work...
Please DO NOT Cheat YOUR SELF !!!
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Hey Now... Do Not DOOO it !!!
Don't CHEAT your OWN Self !!!
Dont scroll down until you have really tried.
Once you HAVE tried, then USE this as your TEMPLATE for other Questions like it
Prob 1, Page xyz
A picture frame has a total perimeter of 3 feet.
The width of the frame is 0.62 times its length.
Find the dimensions of the frame.
DRAWING - label L and W
L
___
W |___| W
L
P = 3 ft
Formula 1 P = 2W + 2L ft
Formula 2 W = 0.62(L) ft
P = 2W + 2L = 3 ft
2( 0.62(L) ) + 2(L) = 3 ft SUBSTITUTE Formula 2 for W - this is THE KEY !!!
1.24(L) + 2(L) = 3 ft
3.24(L) = 3 ft
L = 3 / 3.24 ft Solve for L
L = 0.9259 ft PRE-rounded answer (Round this to nearest 1/100th)
L = 0.93 ft Rounded answer - circle this INCLUDE YOUR UNITS - or it is WRONG !!!
Therefore:
W = 0.62(L) ft
W = 0.62( 0.9259 ft ) Note! USE the PRE-rounded answer when you substitute
W = 0.5740 ft PRE-rounded answer (Round this to nearest 1/100th)
W = 0.57 ft Rounded answer - circle this INCLUDE YOUR UNITS - or it is WRONG !!!
Check Answer:
P = 2W + 2L = 3 ft
P = 2(0.57 ft) + 2(0.93 ft)
P = 1.14 ft + 1.86 ft
P = 3.00 ft IT CHECKS !!! you get 100% for this problem
I do ONLINE Tutoring - Please hire me if you want more help :)
