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vivado [14]
4 years ago
10

Sammy is trying to determine how many triangles she can create out of a square grid that has a side of 14 inches. Use the image

below to determine the area of the triangle and how many she can cut out.
The area of the triangle is 49 in2, so she can create only 2 triangles.
The area of the triangle is 49 in2, so she can create only 4 triangles.
The area of the triangle is 98 in2, so she can create only 2 triangles.
The area of the triangle is 98 in2, so she can create only 4 triangles

Mathematics
1 answer:
ANTONII [103]4 years ago
3 0
To find the area of the triangle, you use the formula A=bh/2. This gives you the area of 49in^2 for the triangle, eliminating choices C and D. The area of the entire square is 14^2, or 196in^2, which gives us 4 when divided by the area of the triangle, 49in^2. Therefore, the answer is B, or that the area of the triangle is 49in^2 so she can create only 4 triangles.
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\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{cccllll}
&Sides&Area&Volume\\
&-----&-----&-----\\
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\end{array}\\\\
-----------------------------\\\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{\sqrt{9}}{\sqrt{18}}=\cfrac{\sqrt[3]{62}}{\sqrt[3]{x}}

\bf \\\\\\
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\\\\\\
x=\left( \sqrt{2}\cdot \sqrt[3]{62} \right)^3\implies x=\sqrt{2^3}\cdot \sqrt[3]{62^3}\implies x=2\sqrt{2}\cdot 62
\\\\\\
\boxed{x=124\sqrt{2}}
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