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Sphinxa
1 month ago
11

The height of a triangular road sign is 1 inch shorter than twice its base. if the area of the sign is 60 in.2, which equation c

ould be used to find the base (b) of the sign?
Mathematics
1 answer:
Inessa [12.5K]1 month ago
6 0
Comment
Let's first tackle the simplest approach to finding the area of a triangle.

Formula for area is
A = 1/2 b * h

Substituting values
Area = 60 in^2
where b = x
and h = 2x - 1 
Thus, 60 = 1/2 * x * (2x - 1)

Now, we solve
60 = 1/2 * x (2x - 1) Multiply by 2
60 * 2 = x(2x - 1)
120 = x (2x - 1) Expand the brackets.
120 = 2x^2 - x  Subtract 120 from both sides.
2x^2 -  x - 120 = 0 which factors out to
(2x + 15)(x - 8) = 0

Now, solving for x
2x + 15 = 0
2x = - 15
thus, x = -15/2
which yields a negative value, hence discard this solution.

x - 8 = 0
gives us x = 8 

Area verification
base = 8
height = 16 - 1 = 15

thus Area = 1/2 * 8 * 15 = 60 confirming the calculation

Response
Utilize Area = 1/2 * b * h to determine both the base and height.
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