SOLUTION: hey, could you please solve this problem for me, and thanks, A rectangle, 3cm longer than it is wide, has a diagonal 15cm long. find the dimensions fo the rectangle. i will

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Question 160319: hey,
could you please solve this problem for me, and thanks,
A rectangle, 3cm longer than it is wide, has a diagonal 15cm long. find the dimensions fo the rectangle.
i will be waiting for the answer,
thank you again,
Found 2 solutions by Edwin McCravy, checkley77:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Draw the rectangle and its diagonal, putting
the length 15 on the diagonal:



Label the width w.

Since the length is 3 cm longer than the width,

label the length w%2B3



Erase the upper left half of the rectangle:



That leaves a right triangle, with legs 

matrix%281%2C3%2Cw%2B3%2C%22%2C%22%2Cw%29 and hypotenuse 15.

So we use the Pythagorean theorem:

a%5E2%2Bb%5E2=c%5E2 with matrix%281%2C5%2Ca=%28w%2B3%29%2C%22%2C%22%2Cb=w%2C%22%2C%22%2Cc=15%29

%28w%2B3%29%5E2%2Bw%5E2=15%5E2

%28w%2B3%29%28w%2B3%29+%2B+w%5E2+=+225

%28w%5E2%2B3w%2B3w%2B9%29%2Bw%5E2=225

%28w%5E2%2B6w%2B9%29%2Bw%5E2=225

w%5E2%2B6w%2B9%2Bw%5E2=225

2w%5E2%2B6w%2B9=225

2w%5E2%2B6w-216=0

Divide through by 2:

2w%5E2%2F2%2B6w%2F2-216%2F2=0%2F2

w%5E2%2B3w-108=0

Think of two integers which
have product -108 and combine
to give +3:

They are -9 and +12, so the
left sides factors as:

%28w-9%29%28w%2B12%29=0

Use the zero-factor principle

matrix%282%2C3%2Cw-9=0%2C%22%2C%22%2Cw%2B12=0%2Cw=9%2C%22%2C%22%2Cw=-12%29

We choose the positive value for the width,

Therefore the width = 9cm
and the length = w+3 = 9+3 = 12cm

Edwin

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
L=W+3
HERE YOU HAVE A RIGHT TRIANGLE OF SIDES L & W WITH AN HYPOTENUSE=15
THUS USING THE PYTHAGOREAN THEOREM (A^2+B^2=C^2)WE GET:
(W+3)^2+W^2=15^2
W^2+6W+9+W^2=225
2W^2+6W+9-225=0
2W^2+6W-216=0
2(W^2+3W-108)=0
2(W-9)(W+12)=0
W-9=0
W=9 FOR THE WIDTH
L=9+3=12 FOR THE LENGTH.
PROOF:
9^2+12^2=15^2
81+144=225
225=225