Question

Given right triangle ABC with altitude B D drawn to hypotenuse AC. If AD = 63 and

BD = 21, what is the length of DC?

Answer 1

Step-by-step explanation:

Using similar triangles ADB ~ BDC due to AAS

then 21 is to 63 as DC is to 21

21/63 = DC/21 Multiply both sides of the equation by 21

21* 21 / 63 = DC

DC = 7 units

Answer 2

In a right triangle, we can use the Pythagorean theorem to find the length of DC. By substituting the given values and solving the equation, we find that the length of DC is approximately 20.54.

Step-by-step explanation:

In a right triangle ABC, with altitude BD drawn to hypotenuse AC, we can use the Pythagorean theorem to find the length of DC.

Given that AD = 63 and BD = 21, we can use the Pythagorean theorem:

AC^2 = AD^2 + DC^2.

Substituting the values, we get AC^2 = 63^2 + DC^2.

Since AC is the hypotenuse, we know that AC = √(AD^2 + BD^2).

Solving for AC, we can plug it back into the first equation to solve for DC.

AC = √(63^2 + 21^2)

= √(3969 + 441)

= √4410 ≈ 66.37

Now, we can substitute AC back into our first equation to solve for DC:

66.37^2 = 63^2 + DC^2.

Solving for DC, we get

DC^2 = 66.37^2 - 63^2

= 4390.96 - 3969 = 421.96.

Therefore, the length of DC is approximately √421.96 ≈ 20.54.