An in-ground pond has the shape of a rectangular prism. The pond has a depth of 24 inches and a volume of 72,000 cubic inches. T
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Answer:
Base of triangle = 2.4 Feet and Height of triangle = 10 feet.
Step-by-step explanation:
This problem can be solved by using formula to calculate area of triangle.
<u>Area of triangle = 1/2*(base*height)</u>
given
Let base of triangle B
height if triangle H
according to problem
The height of a triangle is 2 less than 5 times its base
mathematically it can be expressed as
H = 5*B - 2
Given area of triangle= 12 sq feet
Area of triangle = 1/2*(base*height)
=> 12 = 1/2* {B*(5*B-2)}
=> 24 = 5B^2 - 2B
which is a quadratic equation
It can be solved as given below
Since for side of triangle B cannot be negative number hence B= 12/5 = 2.4
Therefore height of triangle = 5*B - 2 = 5*2.4 - 2 = 12 - 2 = 10
Base of triangle = 2.4 Feet and Height of triangle = 10 feet.
Equation which models this situation is