In a right triangle, if the lengths of the legs are in the ratio 3:4, what is th

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Question: In a right triangle, if the lengths of the legs are in the ratio 3:4, what is the length of the hypotenuse if the shorter leg is 9?

Options:

Correct Answer: 15

Solution:

If the shorter leg is 9, the longer leg is (4/3) * 9 = 12. Hypotenuse = √(9² + 12²) = √(81 + 144) = √225 = 15.

In a right triangle, if the lengths of the legs are in the ratio 3:4, what is the length of the hypotenuse if the shorter leg is 9?

In a right triangle, if the lengths of the legs are in the ratio 3:4, what is the length of the hypotenuse if the shorter leg is 9?

Step 1: Identify the lengths of the legs of the triangle. The shorter leg is given as 9.
Step 2: Use the ratio of the legs (3:4) to find the length of the longer leg. Since the shorter leg corresponds to 3 in the ratio, we can set up the equation: longer leg = (4/3) * shorter leg.
Step 3: Substitute the value of the shorter leg into the equation: longer leg = (4/3) * 9.
Step 4: Calculate the longer leg: longer leg = 12.
Step 5: Now, use the Pythagorean theorem to find the hypotenuse. The formula is hypotenuse = √(shorter leg² + longer leg²).
Step 6: Substitute the values into the formula: hypotenuse = √(9² + 12²).
Step 7: Calculate 9² and 12²: 9² = 81 and 12² = 144.
Step 8: Add the squares: 81 + 144 = 225.
Step 9: Take the square root of 225 to find the hypotenuse: hypotenuse = √225.
Step 10: Calculate the square root: hypotenuse = 15.

Right Triangle Properties – Understanding the relationship between the legs and hypotenuse in a right triangle using the Pythagorean theorem.
Ratios – Applying the concept of ratios to determine the lengths of the legs based on the given ratio.