SOLUTION: The dimensions of a door are 3 ft wide by 7 ft 6 in high. If the same amount is added to each dimension of the door, the area is increased by 49 ft2. Find the dimensions of the new

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The dimensions of a door are 3 ft wide by 7 ft 6 in high. If the same amount is added to each dimension of the door, the area is increased by 49 ft2. Find the dimensions of the new      Log On

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Question 1018156: The dimensions of a door are 3 ft wide by 7 ft 6 in high. If the same amount is added to each dimension of the door, the area is increased by 49 ft2. Find the dimensions of the new door. (Round your answer to one decimal place.)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The current area of the door is:
+A+=+3%2A7.5+
+A+=+22.5+ ft2
Let +x+ = the amount in ft added
to both dimensions
+%28+3+%2B+x+%29%2A%28+7.5+%2B+x+%29+=+22.5+%2B+49+
+22.5+%2B+7.5x+%2B+3x+%2B+x%5E2+=+22.5+%2B+49+
+x%5E2+%2B+10.5x+-+49+=+0+
+2x%5E2+%2B+21x+-+98+=+0+
Use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+2+
+b+=+21+
+c+=+-98+
x+=+%28-21+%2B-+sqrt%28+21%5E2-4%2A2%2A%28-98%29+%29%29%2F%282%2A2%29+
x+=+%28-21+%2B-+sqrt%28+441+%2B+784+%29%29+%2F+4+
x+=+%28-21+%2B-+sqrt%28+1225+%29%29+%2F+4+
+x+=+%28+-21+%2B+35+%29+%2F+4+
+x+=+14%2F4+
+x+=+3.5+
+3+%2B+3.5+=+6.5+
+7.5+%2B+3.5+=+11+
The new dimensions are:
6.5 x 11 ft2
-------------
check:
+%28+3+%2B+x+%29%2A%28+7.5+%2B+x+%29+=+22.5+%2B+49+
+%28+3+%2B+3.5+%29%2A%28+7.5+%2B+3.5+%29+=+22.5+%2B+49+
+6.5%2A11+=+71.5+
+71.5+=+71.5+
OK