### Math Notes

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#### Algebra Solutions

##### Topics || Problems

The sides of a triangle are 10, 9 and 15 inches long. In a similar triangle, the longest side is 21 inches long. Find the other side.

Solution:

Since the triangles are similar the ratio and proportion between their corresponding sides is possible.

Let $$h \text{-shortest}$$ and $$i$$ be the lengths of the remaining side of the triangle.

$$\frac{21}{h} = \frac{15}{9}$$

$$h = \frac{21(9)}{15}$$

$$h = 12.6$$

$$\frac{21}{i} = \frac{15}{10}$$

$$i = \frac{21(10)}{15}$$

$$i = 14$$

Thus, the length of the sides of the triangle are 14, 12.6 and 21 inches.