SOLUTION: The length of the base of a rectangle is 3 inches Less than twice the height if the total area of the rectangle is 152 in.² what are the lengths of the base and the height of the

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The length of the base of a rectangle is 3 inches Less than twice the height if the total area of the rectangle is 152 in.² what are the lengths of the base and the height of the      Log On


   

Question 1143666: The length of the base of a rectangle is 3 inches Less than twice the height if the total area of the rectangle is 152 in.² what are the lengths of the base and the height of the rectangle
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +j+ = base in in.
Let +k+ = height in in.
(1) +j+=+2k+-+3+
(2) +j%2Ak+=+152+
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Substitute (1) into (2)
(2) +%28+2k+-+3+%29%2Ak+=+152+
(2) +2k%5E2+-+3k+=+152+
(2) +2k%5E2+-+3k+-+152+
+k+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+k+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%2A2%2A%28-152%29+%29%29%2F%282%2A2%29+
+k+=+%28+3+%2B-+sqrt%28+9+%2B+1216+%29%29%2F+4+
+k+=+%28+3+%2B+sqrt%28+1225+%29+%29%2F4+
+k+=+%28+3+%2B+35+%29+%2F+4+
+k+=+38%2F4+
+k+=+9.5+
and
+j+=+2%2A9.5+-+3+
+j+=+16+
The base is 16
The height is 9.5
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check:
(2) +j%2Ak+=+152+
(2) +16%2A9.5+=+152+
(2) +152+=+152+
OK