SOLUTION: Karens Backyard has a width of 25 meters and a length of 35 meters. SHe wants to put a rectangular flower garden in the middle of the backyard leaving a strip of grass of uniform w

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Karens Backyard has a width of 25 meters and a length of 35 meters. SHe wants to put a rectangular flower garden in the middle of the backyard leaving a strip of grass of uniform w      Log On


   



Question 744337: Karens Backyard has a width of 25 meters and a length of 35 meters. SHe wants to put a rectangular flower garden in the middle of the backyard leaving a strip of grass of uniform width around all sides of the flower garden. If she wants to have 324 square meters of grass what will be the width and length of the garden
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the uniform width of the grass border
The dimensions of the rectangular flower garden
can be expressed as:
width = +25+-+2x+ m
length = +35+-+2x+ m
----------------------
She wants to have +324+ square meters of grass
Her whole backyard has an area of +25%2A35+=+875+ m2
--------------
The area of her garden is +875+-+324+=+551+
Now I can say:
+%28+25+-+2x+%29%2A%28+35+-+2x+%29+=+551+
+875+-+70x+-+50x+%2B+4x%5E2+=+551+
+4x%5E2+-+120x+%2B+875+-+551+=+0+
+4x%5E2+-+120x+%2B+324+=+0+
+x%5E2+-+30x+%2B+81+=+0+
+%28+x+-+3+%29%2A%28+x+-+27+%29+=+0+ ( by inspection )
The width of the border can't be +x+=+27+, since
that is wider than her backyard, so
width = +25+-+2%2A3+=+19+ m
length = +35+-+2%2A3+=+29+ m
--------------------------
check answers:
+%28+25+-+2x+%29%2A%28+35+-+2x+%29+=+551+
+%28+25+-+2%2A3+%29%2A%28+35+-+2%2A3+%29+=+551+
+19%2A29+=+551+
+551+=+551+
OK