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1). x = 2.67 units

2). x = 4.80 units

3). x = 6.00 units

Step-by-step explanation:

1). By applying Pythagoras theorem,

 Hypotenuse² = [Leg(1)]² + [leg(2)]²

  12² = x² + b² [Let the base of both the triangles = b units]

  144 = x² + b² ------(1)

  Similarly, 13² = (x + 3)² + b²

  169 = x² + 6x + 9 + b²

  169 - 9 - 6x = x² + b²

  160 - 6x = x² + b² ------(2)

  From equation (1) and (2)

  144 = 160 - 6x

  6x = 160 - 144

  x =

  x = 2.67 units

2). By applying Pythagoras theorem,

  10² = x² + h² [Let the height of the triangle = h]

  100 = x² + h² ------(1)

  13² = (2x)² + h²

  169 = 4x² + h² -----(2)

  By substituting equation (1) from equation (2),

  169 - 100 = (4x² + h²) - (x² + h²)

  69 = 3x²

  x² = 23

  x = √23

  x = 4.795

  x ≈ 4.80 units

3). By applying Pythagoras theorem,

  9² = x² + h² [Let the height of the triangle = h units]

  81 = x² + h² ------(1)

  7² = (x - 4)² + h²

  49 = x² + 16 - 8x + h²

  49 - 16 = x² + h² - 8x

  33 + 8x = x² + h² -------(2)

  From equation (1) and (2)

  81 = 33 + 8x

  8x = 48

   x = 6.00 units

hello from mrbilldoesmath!

answer:

x - 3

discussion:

x^2 - 9 = (x-3) (x+3)   so

(x^2-9)/ (x + 3) = x-3

you,

mrb