The lengths of the sides of a triangle are 13, 14 and 15 units. Find the shortest side of a similar triangle whose longest side is 21.
just multiply 13 by 21/15, the scaling ratio.
What is the lengths of the sides of the triangle in {6,6,6}
To find the shortest side of a similar triangle, we can use the property of similar triangles that states the ratios of corresponding sides are equal.
First, let's find the ratio between the longest sides of both triangles. The longest side of the first triangle is 15 units, and the longest side of the second triangle is 21 units. The ratio is 21/15, which simplifies to 7/5.
To find the length of the shortest side of the second triangle, we multiply the ratio found above by the length of the shortest side of the first triangle.
The shortest side of the first triangle is 13 units. Multiplying by the ratio, we get:
(7/5) * 13 = 91/5 = 18.2 units.
Therefore, the shortest side of the similar triangle, whose longest side is 21 units, is approximately 18.2 units.
To find the shortest side of a similar triangle, we can use the concept of ratios. In similar triangles, the ratios of the corresponding sides are equal.
Let's set up the ratio for the sides of the original triangle:
Ratio of the corresponding sides: \( \frac{{\text{{Shortest side of original triangle}}}}{{\text{{Longest side of original triangle}}}} = \frac{{\text{{Shortest side of new triangle}}}}{{\text{{Longest side of new triangle}}}} \)
Substituting the values we know:
\( \frac{{x}}{{21}} = \frac{{13}}{{15}} \)
Now, we can solve for \( x \), which represents the shortest side of the new triangle.
Cross-multiplying the equation:
\( 15x = 13 \times 21 \)
\( 15x = 273 \)
Divide both sides by 15:
\( x = \frac{{273}}{{15}} \)
Performing the division, we find:
\( x \approx 18.2 \)
Therefore, the shortest side of the similar triangle is approximately 18.2 units.