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A triangular pyramid is formed from three right triangles as shown below.
Use the information given in the figure to find the length B D
.
If applicable, round your answer to the nearest whole number.
The lengths on the figure are not drawn accurately.

A triangular pyramid is formed from three right triangles as shown below Use the information given in the figure to find the length B D If applicable round your class=

Respuesta :

ΔADC is a right angle triangle, we will use the Pythagorus Theorem to find the length CD.

Formula of the Pythagorus Theorem : 
⇒ a² + b² = c²
⇒ AD² + CD² = AC²

The value of AD is 54 and the value of AC is 90:
54² + CD² = 90²

Solve for CD:
54² + CD² = 90²
CD² = 90² - 54²
CD² = 5184
CD = √5184
CD = 72

ΔADC is also a right angle triangle, we will use the Pythagorus Theorem to find the length BD.

Formula of the Pythagorus Theorem : 
⇒ a² + b² = c²
⇒ BD² + CD² = BC²

The value of CD is 72 and the value of BC is 97:
BD² + 72² = 97²

Solve for BD:
BD² = 97² - 72²
BD² = 4225
BD = √4225
BD = 65

Answer: The length of BD is 65 units.

The length of BD is "65".

We can use the Pythagorean theorem to calculate DC in the triangle ADC because it is a right-angled triangle:

[tex]\to \bold{(AC)^2 = (AD)^2 + (DC)^2}\\\\\to \bold{(90)^2 = (54)^2 + (DC)^2}\\\\\to \bold{8100 = 2916 + (DC)^2}\\\\\to \bold{8100 - 2916 = (DC)^2}\\\\\to \bold{(DC)^2 =5184 }\\\\\to \bold{(DC) =72 }\\\\[/tex]

Now, in triangle BDC, which is likewise a right-angled triangle, we can use the Pythagorean theorem to find BD:

[tex]\to \bold{(BC)^2 = (BD)^2 + (DC)^2}\\\\\to \bold{(97)^2 = (BD)^2 + (72)^2}\\\\\to \bold{9409 = (BD)^2 + 5184}\\\\\to \bold{9409 - 5184= (BD)^2 }\\\\\to \bold{4225= (BD)^2 }\\\\\to \bold{BD= 65}\\\\[/tex]

Therefore the final answer is "65".

Learn more about the Pythagorean theorem:

brainly.com/question/21802681

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