SOLUTION: When you measured your diagonal clothesline across your rectangular porch, you found that it was 1 foot longer than the length of the porch, and 8 ft longer than the width. What ar

Algebra ->  Rectangles -> SOLUTION: When you measured your diagonal clothesline across your rectangular porch, you found that it was 1 foot longer than the length of the porch, and 8 ft longer than the width. What ar      Log On


   

Question 218394: When you measured your diagonal clothesline across your rectangular porch, you found that it was 1 foot longer than the length of the porch, and 8 ft longer than the width. What are the dimensions of your porch?
Found 2 solutions by checkley77, josmiceli:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(x-1)^2+(x-8)^2=x^2
x^2-2x+1+x^2-16x+64=x^2
2x^2-x^2-18x+65=0
x^2-18x+65=0
(x-13)(x-5)=0
x-13=0
x=13 ft. for the diagonal.
Proof:
(13-1)^2+(13-8)^2=13^2
12^2+5^2=169
169=169

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let D= diagonal
Let W= width
Let L= length
D%5E2+=+W%5E2+%2B+L%5E2
given:
D+=+L+%2B+1
D+=+W+%2B+8
----------------
This is 3 equations and 3 unknowns, so it's solvable
L+=+D+-+1
W+=+D+-+8
D%5E2+=+%28D+-+8%29%5E2+%2B+%28D+-+1%29%5E2
D%5E2+=+D%5E2+-+16D+%2B+64+%2B+D%5E2+-+2D+%2B+1
D%5E2+=+2D%5E2+-+18D+%2B+65
D%5E2+-+18D+%2B+65+=+0
Use the quadratic formula
D+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+-18
c+=+65
D+=+%28-%28-18%29+%2B-+sqrt%28+%28-18%29%5E2-4%2A1%2A65+%29%29%2F%282%2A1%29+
D+=+%28+18+%2B-+sqrt%28+324+-+260++%29%29%2F%282%2A1%29+
D+=+%28+18+%2B-+sqrt%28+64+%29%29%2F2+
D+=+%28+18+%2B-+8%29%2F2+
D+=+13
D+=+5
Right away I see that D=5 won't work, since
5ft can't be 8 ft longer than width, so
W+=+D+-+8
W+=+13+-+8
W+=+5
and
L+=+D+-+1
L+=+13+-+1
L+=+12
The dimensions of the porch are 12' x 5'