SOLUTION: I have been working on this math problem and I can't figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Find the dime

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Question 195654This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been working on this math problem and I can't figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!
Find the dimensions of a rectangle having perimeter 14 m and a diagonal of length 5 m. This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
P=2L%2B2W Start with the perimeter formula


14=2L%2B2W Plug in P=14


7=L%2BW Divide every term by 2


7-W=L Subtract W from both sides.


L=7-W Rearrange the terms.


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a%5E2%2Bb%5E2=c%5E2 Move onto the Pythagorean Theorem


L%5E2%2BW%5E2=5%5E2 Plug in a=L, b=W, and c=5


%287-W%29%5E2%2BW%5E2=5%5E2 Plug in L=7-W


%287-W%29%5E2%2BW%5E2=25 Square 5 to get 25


49-14W%2BW%5E2%2BW%5E2=25 FOIL


49-14W%2BW%5E2%2BW%5E2-25=0 Subtract 25 from both sides.


2W%5E2-14W%2B24=0 Combine like terms.


Notice we have a quadratic equation in the form of aW%5E2%2BbW%2Bc where a=2, b=-14, and c=24


Let's use the quadratic formula to solve for W


W+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


W+=+%28-%28-14%29+%2B-+sqrt%28+%28-14%29%5E2-4%282%29%2824%29+%29%29%2F%282%282%29%29 Plug in a=2, b=-14, and c=24


W+=+%2814+%2B-+sqrt%28+%28-14%29%5E2-4%282%29%2824%29+%29%29%2F%282%282%29%29 Negate -14 to get 14.


W+=+%2814+%2B-+sqrt%28+196-4%282%29%2824%29+%29%29%2F%282%282%29%29 Square -14 to get 196.


W+=+%2814+%2B-+sqrt%28+196-192+%29%29%2F%282%282%29%29 Multiply 4%282%29%2824%29 to get 192


W+=+%2814+%2B-+sqrt%28+4+%29%29%2F%282%282%29%29 Subtract 192 from 196 to get 4


W+=+%2814+%2B-+sqrt%28+4+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


W+=+%2814+%2B-+2%29%2F%284%29 Take the square root of 4 to get 2.


W+=+%2814+%2B+2%29%2F%284%29 or W+=+%2814+-+2%29%2F%284%29 Break up the expression.


W+=+%2816%29%2F%284%29 or W+=++%2812%29%2F%284%29 Combine like terms.


W+=+4 or W+=+3 Simplify.


So the widths are W+=+4 or W+=+3


If we plug these widths into L=7-W, we'll get the lengths

L=3 or L=4


So we'll make the length the longer dimension.


So the length is 4 m and the width is 3 m