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# A triangle is cut by a line s parallel to the base in such a way that it divides the side of the triangle into parts in the ratio of 2 : 3. Find the other side of the triangle if it is known that the line s divides it into parts whose length is 5 cm.

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## Answer to a math question A triangle is cut by a line s parallel to the base in such a way that it divides the side of the triangle into parts in the ratio of 2 : 3. Find the other side of the triangle if it is known that the line s divides it into parts whose length is 5 cm.

Hester
4.8
Let's denote the sides of the triangle as follows: Let AB be the base of the triangle, and CD be the line parallel to the base AB that divides the side into parts in the ratio of 2:3. Let $E$ be the point of intersection between CD and $AB$. So, $AE$ represents 2 parts and $EB$ represents 3 parts. Given that the length of the line $CD$ is 5 cm, we can express $AE$ and $EB$ in terms of this information. Let $x$ be the length of $AE$, then $5 - x$ will be the length of $EB$. Since the parts are in the ratio 2:3, we can set up the following proportion: $\frac{x}{5-x} = \frac{2}{3}$ Now, cross-multiply to solve for $x$: $3x = 2$5 - x$$ $3x = 10 - 2x$ $5x = 10$ $x = 2$ So, the length of $AE$ is 2 cm, and the length of $EB$ is $5 - 2 = 3$ cm. Now, you know the lengths of $AE$ and $EB$. If $AC$ is the other side of the triangle, then $AC = AE + EC$. Substitute the values: $AC = 2 + 3 = 5$ Therefore, the length of the other side of the triangle, AC, is 5 cm.
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