Given a right triangle with legs of 5 cm and 30 cm, which triangle is similar?
Responses
A A right triangle with legs of 3 cm and 24 cmA right triangle with legs of 3 cm and 24 cm
B A right triangle with legs of 6 cm and 18 cmA right triangle with legs of 6 cm and 18 cm
C A right triangle with legs of 4 cm and 24 cmA right triangle with legs of 4 cm and 24 cm
D A right triangle with legs of 6 cm and 24 cm...
To determine which triangle is similar to the given triangle, we need to find the ratio of the lengths of corresponding sides.
The given right triangle has legs of 5 cm and 30 cm.
Option A has legs of 3 cm and 24 cm.
The ratio of the lengths of the corresponding sides are 5/3 and 30/24, which simplifies to 5/3 and 5/2. These ratios are not equal, so option A is not similar to the given triangle.
Option B has legs of 6 cm and 18 cm.
The ratio of the lengths of the corresponding sides are 5/6 and 30/18, which simplifies to 5/6 and 5/3. These ratios are not equal, so option B is not similar to the given triangle.
Option C has legs of 4 cm and 24 cm.
The ratio of the lengths of the corresponding sides are 5/4 and 30/24, which simplifies to 5/4 and 5/2. These ratios are equal, so option C is similar to the given triangle.
Option D has legs of 6 cm and 24 cm.
The ratio of the lengths of the corresponding sides are 5/6 and 30/24, which simplifies to 5/6 and 5/2. These ratios are not equal, so option D is not similar to the given triangle.
Therefore, the correct answer is C: A right triangle with legs of 4 cm and 24 cm.