Question

In a right triangle DEF, the length of one base is 8 units, and the hypotenuse is 8√5 units. What is the length of the other base?

A) 4 units
B) 16 units
C) 8 units
D) 4√5 units

Answer 1

The length of the other base in right triangle DEF is 16 units.

Option B is answer.

Step-by-step explanation:

We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two bases. In this case, we know the length of the hypotenuse (8√5) and one base (8).

Let x be the length of the other base.

Applying the Pythagorean theorem:

(8√5)^2 = 8^2 + x^2

64 * 5 = 64 + x^2

320 = 64 + x^2

x^2 = 256

x = √256

x = 16

Therefore, the other base of the triangle has a length of 16 units, making option (B) the correct answer.