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${:[A=235cm^(2)],[235cm^(2)]:} Find the scale factor for each pair of similar figures 11) two triangles with areas 98m^(2) and 200m^(2) 12) two trapezoids with areas 90m^(2) and 10m^(2)$

$\begin{array}{l} A=235 \mathrm{~cm}^{2} \\ 235 \mathrm{~cm}^{2} \end{array}$ $\newline$ Find the scale factor for each pair of similar figures $\newline$ $11$ ) two triangles with areas $98 \mathrm{~m}^{2}$ and $200 \mathrm{~m}^{2}$ $\newline$ $12$ ) two trapezoids with areas $90 \mathrm{~m}^{2}$ and $10 \mathrm{~m}^{2}$

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Math Problems

Grade 8

Checkpoint: Rational and irrational numbers

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\begin{array}{l} A=235 \mathrm{~cm}^{2} \\ 235 \mathrm{~cm}^{2} \end{array}

\newline

Find the scale factor for each pair of similar figures

\newline

11

) two triangles with areas

98 \mathrm{~m}^{2}

and

200 \mathrm{~m}^{2}

\newline

12

) two trapezoids with areas

90 \mathrm{~m}^{2}

and

10 \mathrm{~m}^{2}

Find Scale Factor: To find the scale factor between two similar triangles, we take the square root of the ratio of their areas. $\newline$ So, for the triangles with areas $98\,\text{m}^2$ and $200\,\text{m}^2$ , the scale factor is the square root of $\frac{200\,\text{m}^2}{98\,\text{m}^2}.$
Calculate Scale Factor: Calculating the scale factor for the triangles: $\sqrt{\frac{200}{98}} = \sqrt{2.040816327} \approx 1.42857$ .
Find Scale Factor: For the trapezoids with areas $90\,\text{m}^2$ and $10\,\text{m}^2$ , we again take the square root of the ratio of their areas to find the scale factor. $\newline$ So, the scale factor is the square root of $10\,\text{m}^2$ divided by $90\,\text{m}^2$ .
Calculate Scale Factor: Calculating the scale factor for the trapezoids: $\sqrt{\frac{10}{90}} = \sqrt{\frac{1}{9}} = \frac{1}{3} \approx 0.33333$ .