Since the height of an equilateral triangle in terms of its side s is s√3/2, the height of the triangle is 6√3/2 = 3√3 and so the area is (1/2)(6)(3√3) = 9√3.
<span>If we draw a horizontal line a height of h from the base of the triangle, the region is split into two regions: the lower region consisting of a trapezoid of height h and the upper region consisting of a triangle of height 3√3 - h. </span>
<span>Since the upper triangle and the triangle itself are similar triangles, the base and height are proportional. If we let x denote the base of the length of the upper triangle, we have: </span>
<span>(S. of small triangle)/(S. of big triangle) = (Ht. of small triangle)/(Ht. of big triangle) </span>
<span>==> x/6 = (3√3 - h)/(3√3) </span>
<span>==> x = (6√3 - 2h)/√3 </span>
<span>Thus, the area of the upper triangle is: </span>
<span>A = (1/2)[(6√3 - 2h)/√3](3√3 - h) = [(6√3 - 2h)(3√3 - h)]/(2√3). </span>
<span>(Made a dumb mistake about the height here for some reason) </span>
<span>Since we require that the area of this triangle is to be half of the total area (9√3/2), we need to solve: </span>
<span>[(6√3 - 2h)(3√3 - h)]/(2√3) = 9√3/2 </span>
<span>==> (6√3 - 2h)(3√3 - h) = 27 </span>
<span>==> 54 - 6h√3 - 6h√3 + 2h^2 = 27 </span>
<span>==> 2h^2 - 12h√3 + 27 = 0. </span>
<span>Solving with the Quadratic Formula gives: </span>
<span>h = (6√3 + 3√6)/2 ≈ 8.87 units and h = (6√3 - 3√6)/2 ≈ 1.52 units. </span>
<span>Since h = (6√3 + 3√6)/2 would place the line outside of the triangle, we pick h = (6√3 - 3√6)/2. </span>
<span>Therefore, the line should be ==> (6√3 - 3√6)/2 units from the base. </span>
<span>I hope this helps! ^^ Brainliest Please?</span><span>
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The answer is D.
The first step is to use the distributive property and turn 5(x-4) into 5x - 20.
You then move the twenty into the right equation by adding 20 to both sides. The final step is to move the 3x into the left equation by subtraction and then dividing both sides by 2 to isolate x. Hope this helped !!
Answer:
2k-58
Step-by-step explanation:
-5(k+6) + 7(k-4)
-5k-30+7k-28
2k-48
Answer:
(-1,-5)
Step-by-step explanation:
Solve by substitution
