Question

Solve for the length of AD.

32 cm
16 cm
27 cm

Answer 1

The length of AD is approximately 35.78 cm.

Step-by-step explanation:

To solve for the length of AD, we can use the Pythagorean theorem, which states that in a right-angled 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. In this case, we have a right-angled triangle with sides of 32 cm and 16 cm. Therefore, using the Pythagorean theorem, we can calculate the length of AD as follows:

AD² = AB² + BD² AD² = (32 cm)² + (16 cm)² AD²= 1024 cm² + 256 cm² AD² = 1280 cm²

Taking the square root of both sides gives us: AD = √1280 cm AD ≈ 35.78 cm

However, since AD is a length in a triangle, it cannot be negative. Therefore, we take the positive value: AD ≈ 35.78 cm

Therefore, the length of AD is approximately 35.78 cm.

Answer 2

In this right triangle, the length of AD is approximately 27 cm.

The answer is option ⇒4

Step-by-step explanation:

To solve for the length of AD, we can use the Pythagorean theorem in triangle ACD. Given that AC = 32 cm, AD = x cm, and CD = 16 cm, we can set up the equation AC² = AD² + CD².

Plugging in the values, we have:

32² = x² + 16²

Simplifying the equation:

1024 = x² + 256

To isolate x², we subtract 256 from both sides:

x² = 1024 - 256

x² = 768

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

x ≈ √768

Calculating this, we find x ≈ 27 cm.

Therefore, the length of AD is approximately 27 cm.

The answer is option ⇒4

Your question is incomplete, but most probably the full question was:

See the right triangle below:

Solve for the length of AD.

Given: AC = 32 cm, CD = 16 cm

Options:

• 18 cm
• 32 cm
• 16 cm
• 27 cm