23. Two similar triangles have areas of 76 square centimeters and 931 square centimeters. Determine the ratio of their perimeters. 24. Justify The endnoints.

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To determine the ratio of the perimeters of two similar triangles, we can use the fact that the ratio of the areas of similar figures is equal to the square of the ratio of their corresponding sides.

Given:
- Area of the first triangle = 76 square centimeters
- Area of the second triangle = 931 square centimeters

Let's denote the ratio of the perimeters of the two triangles as $$ r $$.

The ratio of the areas of the two triangles is given by:
$$ \frac{76}{931} = \left(\frac{r}{1}\right)^2 $$

Now, we can solve for $$ r $$ to find the ratio of their perimeters.
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
  $$\frac{76}{931}=\left(\frac{r}{1}\right)^{2}$$
- step1: Reduce the fraction:
  $$\frac{4}{49}=r^{2}$$
- step2: Swap the sides:
  $$r^{2}=\frac{4}{49}$$
- step3: Simplify the expression:
  $$r=\pm \sqrt{\frac{4}{49}}$$
- step4: Simplify the expression:
  $$r=\pm \frac{2}{7}$$
- step5: Separate into possible cases:
  $$\begin{align}&r=\frac{2}{7}\&r=-\frac{2}{7}\end{align}$$
- step6: Rewrite:
  $$r_{1}=-\frac{2}{7},r_{2}=\frac{2}{7}$$
The ratio of the perimeters of the two similar triangles is $$ \frac{2}{7} $$ or approximately 0.2857.
The ratio of the perimeters of the two similar triangles is 2:7.

Two similar triangles have areas of 76 square centimeters and
931 square centimeters. Determine the ratio of their perimeters.

Justify The endnoints.

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Two similar triangles have areas of 76 square centimeters and 931 square centimeters. Determine the ratio of their perimeters. Justify The endnoints.