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.(1 point)
The smaller side length is___ inches and the larger side length is___ inches
To find the lengths of the other two sides of the similar triangle, we can set up a proportion using the corresponding sides of the two triangles.
Let's set up the proportion:
$\dfrac{\text{length of smaller side of new triangle}}{\text{length of smallest side of original triangle}} = \dfrac{\text{length of other side of new triangle}}{\text{length of other side of original triangle}}$
Plugging in the given values, we have:
$\dfrac{1.4}{4.2} = \dfrac{\text{length of other side of new triangle}}{5.7} \implies \text{length of other side of new triangle} = \dfrac{1.4}{4.2} \cdot 5.7$
Calculating this, we get:
$\text{length of other side of new triangle} \approx 1.9$ inches
Therefore, the lengths of the other two sides of the similar triangle are approximately 1.4 inches and 1.9 inches.