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nignag [31]
4 years ago
15

Given the volume of Figure A is 512cm ^3and Figure B is 343cm^3, find the ratio of the perimeter from Figure A to Figure B.

Mathematics
1 answer:
sp2606 [1]4 years ago
5 0

\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\[2em] \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ \cline{2-4}&\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\[-0.35em] ~\dotfill

\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}

\bf \cfrac{\textit{figure A}}{\textit{figure B}}\qquad \qquad \cfrac{s}{s}=\cfrac{\sqrt[3]{512}}{\sqrt[3]{343}}\qquad \begin{cases} 512=&2^9\\ &2^{3\cdot 3}\\ &(2^3)^3\\ 343=&7^3 \end{cases}\implies \cfrac{s}{s}=\cfrac{\sqrt[3]{(2^3)^3}}{\sqrt[3]{7^3}} \\\\\\ \cfrac{s}{s}=\cfrac{2^3}{7}\implies \cfrac{s}{s}=\cfrac{8}{7}\implies s:s = 8:7\impliedby \textit{ratio of the }\stackrel{sides~and}{perimeters}

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3 years ago
Some help would be good
LekaFEV [45]

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4 years ago
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7 0
4 years ago
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Answer:

The Proof is given below.

Step-by-step explanation:

Given:

\overline{HF}  bisect ∠ EHG.i.e

∴ ∠EHF ≅ ∠ GHF

\overline{EH} \cong \overline{GH}  

To Prove:

\overline{EF} \cong \overline{GF}  

Proof:

In  Δ EHF and Δ GHF

    EH ≅ GH     ………............{Given}

∠ EHF ≅ ∠ GHF     …………..{EF bisect ∠ EHG as given above}

     HF ≅ HF     ………............{Reflexive Property}

Δ EHF ≅ Δ GHF …................{ By Side-Angle-Side test}

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\overline{EF} \cong \overline{GF}  ....... PROVED

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4 years ago
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