SOLUTION: Jessica wants to build a tool shed in her backyard but is only using the area beyond the path running through the yard. How large would the shed be it is triangular-shaped with sid

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Question 1034780: Jessica wants to build a tool shed in her backyard but is only using the area beyond the path running through the yard. How large would the shed be it is triangular-shaped with sides of length 8 feet, 15 feet, and 20 feet
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the sides:
+a+=+8+
+b+=+15+
+c+=+20+
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Call +h+ the perpendicular from
the junction of +a+ and +b+
to side +c+
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+h+ divides +c+ into
+x+ and +c+-+x+
------------------------
+h%5E2+=+a%5E2+-+x%5E2+
and
+h%5E2+=+b%5E2+-+%28+c+-+x+%29%5E2+
--------------------------
+a%5E2+-+x%5E2+=+b%5E2+-+%28+c+-+x+%29%5E2+
Plug in the numbers
+8%5E2+-+x%5E2+=+15%5E2+-+%28+20+-+x+%29%5E2+
+64+-+x%5E2+=+225+-+%28+400+-+40x+%2B+x%5E2+%29+
+64+-+x%5E2+=+225+-+400+%2B+40x+-+x%5E2+%29+
+64+=+-175+%2B+40x+
+40x+=+239+
+x+=+5.975+
and
+h%5E2+=+a%5E2+-+x%5E2+
+h%5E2+=+8%5E2+-+5.975%5E2+
+h%5E2+=+64+-+35.7+
+h%5E2+=+28.3+
+h+=+5.32+
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Let area = +A+
+A+=+%281%2F2%29%2Ac%2Ah+
+A+=+%281%2F2%29%2A20%2A5.32+
+A+=+53.2+
The area is 53.2 ft2
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Definitely get another opinion on this
if you can -I could easily have messed up
the calculations