A right isosceles triangle has side lengths of 13.2, 13.2, and 18.6 meters. What is the hypotenuse of a similar triangle with legs 4.4 meters in length?
The ratio of corresponding side lengths in similar triangles is equal. Let the hypotenuse of the similar triangle be $x$. Setting up a proportion, we have $\frac{13.2}{18.6}=\frac{4.4}{x}$. Cross-multiplying gives $13.2x=(18.6)(4.4)$. Dividing both sides by $13.2$ to solve for $x$ gives $x=\frac{(18.6)(4.4)}{13.2}=\boxed{6.2}$.
A quadrilateral’s smallest side measures 29 mm and its largest side measures 38 mm. A similar quadrilateral’s largest side measures 95 mm. What is the measure of its smallest side?
The ratio of corresponding side lengths in similar quadrilaterals is equal. Let $x$ be the measure of the smallest side in the similar quadrilateral. We set up a proportion: $\frac{29}{38}=\frac{x}{95}$. Cross-multiplying gives $29(95)=38x$. Dividing both sides by 38 gives $x=\frac{29(95)}{38} = \boxed{72.5}$ mm.
A triangle has sides of lengths 4.2, 5.7, and 7.2 inches. The smallest side of a similar triangle is 1.4 inches. What are the lengths of the other two sides? Write the smaller side length first and the larger side length second.
To find the ratio of the lengths of the corresponding sides of the two similar triangles, we divide the length of the smallest side of the original triangle (4.2 inches) by the length of the smallest side of the similar triangle (1.4 inches):
$$\text{Ratio} = \frac{4.2 \text{ inches}}{1.4 \text{ inches}} = 3.$$
The ratio tells us that the lengths of the corresponding sides of the two triangles are multiples of 3.
To find the lengths of the other two sides of the similar triangle, we multiply the length of each corresponding side of the original triangle by 3:
$$(4.2 \text{ inches}) \cdot 3 = 12.6 \text{ inches},$$
$$(5.7 \text{ inches}) \cdot 3 = 17.1 \text{ inches}.$$
Therefore, the lengths of the other two sides of the similar triangle are $12.6$ inches and $17.1$ inches, with the smaller side length first and the larger side length second.
wrong
I apologize for the mistake. To find the lengths of the other two sides of the similar triangle, we need to multiply the length of each corresponding side of the original triangle by the same scale factor.
Let the lengths of the other two sides of the similar triangle be $x$ inches and $y$ inches. The ratio of the lengths of the corresponding sides is given by:
$$\frac{x}{4.2} = \frac{y}{5.7} = \frac{1.4}{7.2}.$$
Simplifying, we find:
$$\frac{x}{4.2} = \frac{1.4}{7.2} \implies x = \frac{1.4}{7.2} \cdot 4.2 = 0.819$$
$$\frac{y}{5.7} = \frac{1.4}{7.2} \implies y = \frac{1.4}{7.2} \cdot 5.7 = 1.113.$$
Therefore, the lengths of the other two sides of the similar triangle are approximately $0.819$ inches and $1.113$ inches, with the smaller side length first and the larger side length second.