Mathematics, 27.06.2019 15:00 diamontehunter1632

Hi any chance that somebody can me with 9, 10, and 11? u so much for your if you know ! ❤️

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Answer from: kkmonsterhigh18

✿ Heya! Grace ✿

✿ Nice Flower Drawing ✿

9. Given : The Length of the Side of the Square is $\mathsf{: 48\sqrt{2}}$

We know that : Area of a Square is given by : Side × Side

$\mathsf{\implies The\;Area\;of\;the\;Given\;Square = (48\sqrt{2}) \times (48\sqrt{2})}$

$\mathsf{\implies The\;Area\;of\;the\;Given\;Square = (48\sqrt{2})^2}$

$\mathsf{\implies The\;Area\;of\;the\;Given\;Square = (48)^2(2)}$

$\mathsf{\implies The\;Area\;of\;the\;Given\;Square = (2304)(2)}$

$\mathsf{\implies The\;Area\;of\;the\;Given\;Square = 4608\;Inch^2}$

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10. Given : The Length of Rectangular Prism $\mathsf{= \sqrt{5}\;feet}$

Given : The Width of Rectangular Prism $\mathsf{= 2 + \sqrt{3}\;feet}$

Given : The Height of Rectangular Prism $\mathsf{= 2 - \sqrt{3}\;feet}$

We know that : Volume of a Rectangular Prism is given By :

✿ Length × Width × Height

⇒ Volume of the Given Rectangular Prism is :

✿ $\mathsf{(\sqrt{5}) \times (2 + \sqrt{3}) \times (2 - \sqrt{3})}$

$\mathsf{\implies (\sqrt{5}) \times (2^2 - (\sqrt{3})^2)}$

$\mathsf{\implies (\sqrt{5}) \times (4 - 3)}$

$\mathsf{\implies \sqrt{5}}$

-------------------------------------------------------------

11. (a)

Given : The Length of First Leg $\mathsf{= 3 + \sqrt{3}\;feet}$

Given : The Length of Second Leg $\mathsf{= 3 - \sqrt{3}\;feet}$

We know that, From Pythagorean Theorem :

✿ (Hypotenuse)² = (First Leg)² + (Second Leg)²

$\mathsf{\implies (Hypotenuse)^2 = (3 + \sqrt{3})^2 + (3 - \sqrt{3})^2}$

$\mathsf{\implies (Hypotenuse)^2 = (3^2 + (\sqrt{3})^2 + 2(3)(\sqrt{3}) + (3^2 + (\sqrt{3})^2 - 2(3)(\sqrt{3})}$

$\mathsf{\implies (Hypotenuse)^2 = [3^2 + (\sqrt{3})^2] + [3^2 + (\sqrt{3})^2]}$

$\mathsf{\implies (Hypotenuse)^2 = (2) [3^2 + (\sqrt{3})^2]}$

$\mathsf{\implies (Hypotenuse)^2 = (2) [9 + 3]}$

$\mathsf{\implies (Hypotenuse)^2 = (2)(12)}$

$\mathsf{\implies (Hypotenuse)^2 = 24}$

$\mathsf{\implies Hypotenuse = \sqrt{24}}$

$\mathsf{\implies Hypotenuse = 2\sqrt{6}}$

(b). We know that Perimeter of a Triangle is given by Adding the Lengths of all the Three Sides of the Triangle.

$\mathsf{\implies Perimeter\;of\;the\;Given\;Triangle = [(3 + \sqrt{3}) + (3 - \sqrt{3}) + 2\sqrt{6}]}$

$\mathsf{\implies Perimeter\;of\;the\;Given\;Triangle = [(3 + 3 + 2\sqrt{6}]}$

$\mathsf{\implies Perimeter\;of\;the\;Given\;Triangle = (6 + 2\sqrt{6})\;feet}$

(c). We know that : Area of a Triangle is given by :

✿ $\mathsf{\frac{1}{2} \times Base \times Height}$

$\mathsf{\implies Area\;of\;Given\;Triangle = \frac{1}{2}(3 + \sqrt{3})(3 - \sqrt{3})}$

$\mathsf{\implies Area\;of\;Given\;Triangle = \frac{1}{2}[3^2 - (\sqrt{3})^2]}$

$\mathsf{\implies Area\;of\;Given\;Triangle = \frac{1}{2}[9 - 3]}$

$\mathsf{\implies Area\;of\;Given\;Triangle = \frac{1}{2}(6)}$

$\mathsf{\implies Area\;of\;Given\;Triangle = 3\;feet^2}$

Answer from: Quest

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step-by-step explanation:

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Answer from: Quest

tell you what. i'll find the length of the medians and you can fill in the blanks where they belong.

b = (2a,0)

r = (a/2,b/2) remember these things are medians. they go to the 1/2 way point of the line opposite the vertex they face.

br^2 = (2a - a/2)^2 + (0 - b/2)^2

br^2 = (3/2 a) ^2 + b^2 / 4

br^2 = 9/4 a^2 + b^2 / 4 we need to find some relationship between a and b.

let's try ab = bc

ab = 2a

bc = (2a - a)^2 + (b - 0)^2

bc = sqrt(a^2 + b^2)

ab = bc

2a = sqrt(a^2 + b^2) square both sides.

4a^2 = a^2 + b^2 subtract a^2 from both sides.

sqrt(3a^2) = sqrt(b^2)

sqrt(3)a = b

let's put b into br^2

br^2 = 9/4 a^2 + 3b^2 / 4

br^2 = 12 a^2 / 4

br^2 = 3a^2

br = sqrt(3) * a

c = (a,b) ; p = (a,0) this is another application of the distance formula, and it is a good one.

cp^2 = (a - a)^2 + (b - 0)^2

cp^2 = 0 + b^2

cp^2 = b^2 which you can see from the diagram.

cp = sqrt(b^2)

cp = b but b = sqrt(3) * a

cp = sqrt(3)*a

a = (0,0)

q = (3/2) a, b/2

aq^2 = (3a/2 -0)^2 + (b/2 - 0)^2

aq^2 = 9a^2/4 + b^2/4

but b = sqrt(3) * a

aq^2 = 9a^2 / 4 + (sqrt(3)*a)^2 /4

aq^2 = 9 a^2/ 4 + 3 a^2 / 4

aq^2 = 12 a^2/4

aq^2 = 3 a^2

aq = (sqrt 3) * a which agrees with the other two.

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Hi any chance that somebody can me with 9, 10, and 11? u so much for your if you know ! ❤️

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