The height of a triangle is 5 m less than half its base. If the area of the triangle is 300 m2, how do you find the measure of the height?

Answer 1

height#=15" meters"#

The formula for area of the triangle is #A = (bh)/2#.
Let the base be #b# and the height be #b/2 - 5#.

Then:

#300 = (b(b/2 - 5))/2#
#600 = b(b/2 - 5)#
#600 = b^2/2 - 5b#
#600 = (b^2 - 10b)/2#
#1200 = b^2 - 10b#
#b^2 - 10b - 1200= 0#

Solve by completing the square:

#1(b^2 - 10b + 25 -25) = 1200#
#1(b^2 - 10b + 25) - 25 = 1200#
#(b - 5)^2 = 1225#
#b - 5 = +-35#
#b = -30 and 40#

Hence, the base measures #40" meters" (a negative length is impossible).

The height therefore measures #40/2 - 5 = color(green)(15)#

Hopefully this helps!

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Answer 2

Let (h) be the height of the triangle and (b) be the base. We are given that the height is 5 meters less than half the base, so we can write the equation:

[ h = \frac{b}{2} - 5 ]

The area of a triangle can be calculated using the formula:

[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} ]

Substituting the given values, we have:

[ 300 = \frac{1}{2} \times b \times \left(\frac{b}{2} - 5\right) ]

Solving this equation will give us the value of (b), the base of the triangle. Once we have (b), we can substitute it back into the equation for the height to find the value of (h).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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