Question

In triangle △JKL, ∠JKL is a right angle, and KM is an altitude. (JK = 24) and (JM = 18), find (JL).

a) 30
b) 36
c) 42
d) 48

Answer 1

Using the Pythagorean theorem on a right-angled triangle △JKL with sides JK = 24 and JM = 18, we find that the hypotenuse JL equals 30 units. Therefore, the answer is option (a).

Step-by-step explanation:

To solve for the length of side JL in triangle △JKL, where ∠JKL is a right angle and KM is an altitude, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We are given JK = 24 units and JM = 18 units. Since KM is the altitude, JM is part of the hypotenuse JL, and JK is a side of the triangle.

We can apply the Pythagorean theorem as follows:

JK2 + JM2 = JL2

242 + 182 = JL2

576 + 324 = JL2

900 = JL2

To find JL, we take the square root of both sides:

√900 = JL

30 = JL

The length of side JL is therefore 30 units, which corresponds to option (a).