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Find the missing length indicated. i’ve been really struggling with this for some reason, i just don’t understand at all.

Find the missing length indicated ive been really struggling with this for some reason i just dont understand at all class=

Respuesta :

MisterBrian

Answer:

60 units

Step-by-step explanation:

Mark the angles as shown.

Given BC = x

  • MC = 36

Let us assume:

  • AB = y
  • BC = x
  • BM = m
  • MC = 36
  • AM = 64

Baudhayan theorem states that

  • Hypotenuse ² = Base² + Perpendicular ² with respect to ∅

In ∆ BMC,<BMC = 90°. So by Baudhayan theorem

  • BC² = MC²+BM²
  • x² = 36² + m² ...(i)

In ∆BMA <BMA = 90° . So by Baudhayan theorem

  • AB² = BM² + AM²
  • y² = m² + 64² ...(ii)

In ∆ ABC <ABC = 90°. So by Baudhayan theorem

  • AC² = BC² + AB²

Here AC = AM + CM = 64+36 = 100

  • 100² = x² + y² ...(iii)

Add equation (i) and (ii):

  • x²+ y² = 36²+64²+2m²

From equation (iii),

  • 100² = 1296 + 4096 + 2m²
  • 10000 = 5392 +2m²

Subtract 5392 from both sides:

  • 4608 = 2m²

Divide both sides by 2:

  • 4608/2 = m² = 2304

Square root both sides:

  • m = √2304 = 48

Putting the value of m in equation (i),

  • x² = 36² + 48² = 1296 + 2304 = 3600 = 60²

Square root both sides:

  • x = 60 units
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