Using the geometric mean and Pythagorean theorem, calculate the values of the missing sides. Round your answers to the thousandt
hs place (3 decimal places).
1 answer:
Answer:
a = 9.849
b = 20.25
c = 491.03
Step-by-step explanation:
By using Pythagoras theorem in the right triangle BDC,
(Hypotenuse)² = (Leg 1)² + (Leg 2)²
BC² = BD² + DC²
a² = 9² + 4²
a =
a =
a = 9.8489
a ≈ 9.849 units
By mean proportional theorem,
AD × DC = BD²
b × 4 = 9²
b =
b = 20.25 units
BY Pythagoras theorem in ΔADB,
AB² = AD² + BD²
c² = b² + 9²
c² = (20.25)² + 9²
c² = 410.0625 + 81
c = 491.0625
c = 491. 063 units
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Answer:
Base = 24 cm or 10cm
Step-by-step explanation:
REMEMBER:
An isosceles triangle ABC with base BC = ‘b' & height AD = ‘h' & its equal sides =13 cm & area = 60 cm²
Using the formulas
There are 2 solutions for
≈
Less complex:
Area of a triangle = 1/2 * b * h = 60
=> h = 120/b
In right triangle ABD
13² = h² + b² /4 ( by Pythagoras law)
=>169 = 120²/b² + b²/4
=>676 b² = 57600 + b^4
=> b^4 - 676 b² + 57600 = 0
=> b² = 676 +- √(676² - 4*57600) / 2
=> b²= 676 +- √(226576) /2
=> b² = (676 +- 476 )/2
=> b² = 1152/2 , 200 /2
=> b² = 576 , 100
=> b = 24, 10
So, Base = 24 cm or 10cm