Question

A triangular pyramid is formed from three right triangles as shown below.

Answer 1

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.