The area of a triangle is 16 units square. The length is twice the height. Find the height

Mathematics

1 answer:

Norma-Jean [14]3 years ago

8 0

The formula for area of a triangle is 1/2 x base x height.

Let the height = x

Then the base (length) = 2x ( twice the height)

You know have 16 = 1/2 * 2x * x

Multiply both sides by 2 to remove the 1/2:

32 = 2x * x

Simplify the right side:

32 = 2x^2

Divide both sides by 2:

16 = x^2

Take the square root of both sides:

X = 4

The height is 4 units and the length is 8 Units

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Please help with this question!!

xxMikexx [17]

$\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2\\\\l\perp k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\\text{We have the points J(-24, -4) and K(-4, 6)}.\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{substitute:}\\\\m_1=\dfrac{6-(-4)}{-4-(-24)}=\dfrac{10}{20}=\dfrac{1}{2}\\\\\text{therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-2\\\\\text{The formula of a midpoint:}\\\\\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)\\\\\text{substitute the coordinates of the points J and K:}$

$x=\dfrac{-24+(-4)}{2}=\dfrac{-28}{2}=-14\\\\y=\dfrac{-4+6}{2}=\dfrac{2}{2}=1\\\\\text{midpoint}\ (-14,\ 1)\\\\\text{The point-slope form:}\\\\y-y_1=m(x-x_1)\\\\\text{substitute}\ m=-2,\ x_1=-14\ \text{and}\ y_1=1:\\\\y-1=-2(x-(-14))\\\\\boxed{y-1=-2(x+14)}$