Question

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

Answer 1

✿ 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 :

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

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

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

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

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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 :

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

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

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

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

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

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