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# Similar triangles

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the ratios of the measures of the sides of a triangle is 2:10:7. Find the length of each side if the perimeter of the triangle is 228 meters

Jan 17, 2019

#1
+111357
+2

We have   2 + 10 + 7 =   19 equal parts

So

One side  =  (2/19) * 228  =   24

The next side is 10 : 2 =   5 times this =  120

So...the remaining side  =  228 - 120 - 24   =  84

Jan 17, 2019
#2
+24857
+8

The ratios of the measures of the sides of a triangle is 2:10:7.
Find the length of each side if the perimeter of the triangle is 228 meters.

$$\begin{array}{|rclcl|} \hline a+b+c &=& 228 \quad & | & \quad \dfrac{c}{a} = \dfrac{7}{2} \Rightarrow \boxed{c=\dfrac{7}{2}a } \\ & & \quad & | & \quad \dfrac{a}{b} = \dfrac{2}{10} \Rightarrow \boxed{b=\dfrac{10}{2}a } \\ a+\dfrac{10}{2}a+\dfrac{7}{2}a &=& 228 \\ \dfrac{19}{2}a &=& 228 \\ a &=& \dfrac{228\cdot 2}{19} \\ \mathbf{a} & \mathbf{=} & \mathbf{24} \\\\ 24+b+c &=& 228 \\ b+c &=& 228-24 \\ b+c &=& 204 \quad & | & \quad \dfrac{b}{c} = \dfrac{10}{7} \Rightarrow \boxed{b=\dfrac{10}{7}c } \\ \dfrac{10}{7}c+c &=& 204 \\ \dfrac{17}{7}c &=& 204 \\ c &=& \dfrac{204\cdot 7}{17} \\ \mathbf{c} & \mathbf{=} & \mathbf{84} \\\\ b &=& \dfrac{10}{2}a\\ b &=& 5a\\ b &=& 5\cdot 24 \\ \mathbf{b} & \mathbf{=} & \mathbf{120} \\ \hline \end{array}$$

Jan 17, 2019