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Mathematics

1 answer:

Maurinko [17]2 years ago

4 0

Answer:

see explanation

Step-by-step explanation:

Calculate the distance d using the distance formula

d = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = ((- 2, - 3 ) and (x₂, y₂ ) = (x, 5x + 9 )

d = $\sqrt{(x-(-2))^2+(5x+9-(-3))^2}$

= $\sqrt{(x+2)^2+(5x+9+3)^2}$

= $\sqrt{(x+2)^2+(5x+12)^2}$

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The area of the following equilateral triangle is 62.4 square feet that is he height

Vikentia [17]

The height of this triangle would be 10.4

In order to find this, you first must find the length of the sides. Using a manipulated formula for area of an equilateral triangle, we can determine the lengths of the side. Below if the formula.

S = $\frac{2}{3}3^{\frac{3}{4}} \sqrt{A}$

In this, S is the length of the side and A is the area. So we plug in and get:

S = $\frac{2}{3}3^{\frac{3}{4}} \sqrt{62.4}$

S = $\frac{2}{3}3^{\frac{3}{4}} 7.89$

S = 12

Now that we have the side as 12, we can use the Pythagorean Theorem to find the height. If you split a equilateral triangle down the middle, you are left with two right triangles. Using this right triangle, the hypotenuse would be 12, the first leg would be 6 (half of the base) and the height would be the other leg. So we plug in and solve.

$a^{2} + b^{2} = c^{2}$