SOLUTION: The height of a triangle is 4 m more than twice the length of the base. The area is 15m2. Find the height of the triangle.
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Question 987518: The height of a triangle is 4 m more than twice the length of the base. The area is 15m2. Find the height of the triangle.
Answer by algebrahouse.com(1659) (Show Source): You can put this solution on YOUR website!
base x height
------------- = area of a triangle
2
b = base
2b + 4 = height {the height is 4 more than twice the base}
b(2b + 4)
--------- = 15 {substituted base and height into area formula}
2
b(2b + 4) = 30 {multiplied each side by 2}
2bē + 4b = 30 {used distributive property}
bē + 2b = 15 {divided entire equation by 2}
bē + 2b - 15 = 0 {subtracted 15 from each side}
(b + 5)(b - 3) = 0 {factored into two binomials}
b + 5 = 0 or b - 3 = 0 {set each factor equal to 0}
b = -5 or b = 3 {subtracted 5 and added 3 to the equations}
base cannot be -5
base = 3 m
height = 10 m {since 2b + 4 was the height}
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