contestada

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If
AD = 15 and DC = 11, what is the length of BD in simplest radical
form?
B
A
15
C
X
D
11

Respuesta :

Answer:

BD = √165

Step-by-step explanation:

Drawing the figure : (See attached, figure not to scale)

Solving :

We can make equations based on the Pythagorean Theorem based on the 3 right triangles :

  1. BD² + 15² = AB²
  2. BD² + 11² = BC²
  3. AB² + BC² = 26²

Substitute Equation 1 and 2 in Equation 3 :

⇒ (BD² + 15²) + (BD² + 11²) = 26²

⇒ 2BD² + 225 + 121 = 676

⇒ 2BD² + 346 = 676

⇒ 2BD² = 330

⇒ BD² = 165

⇒ BD = √165

Ver imagen Аноним
semsee45

Answer:

[tex]\sf BD=\sqrt{165}[/tex]

Step-by-step explanation:

Altitude:  A line segment drawn from a vertex that is perpendicular to the side opposite that vertex.

By drawing the altitude, the two internal triangles formed are similar to the original triangle.  If two triangles are similar, their sides are proportional in length:

[tex]\implies \sf segment : altitude = altitude : segment[/tex]

[tex]\implies \sf \dfrac{segment}{altitude}=\dfrac{altitude}{segment}[/tex]

[tex]\implies \sf \dfrac{DC}{BD}=\dfrac{BD}{AD}[/tex]

[tex]\implies \sf \dfrac{11}{BD}=\dfrac{BD}{15}[/tex]

[tex]\implies \sf 11 \cdot 15=BD^2[/tex]

[tex]\implies \sf BD^2=165[/tex]

[tex]\implies \sf BD=\sqrt{165}[/tex]

(Refer to attached diagram - drawn to scale)

Ver imagen semsee45

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