if ABCD is a rectangle and P is a point inside it such that AP =33, BP=16,DP=63. find CP
Answers
Answer:
46.
Step-by-step explanation:
Given,
AP=33, BP=16, DP=63,CP=?
We know that the diagonals of a rectangle are equal.
Hence,
BP + DP = AP + CP
16 + 63 = 33 + x
79 = 33 + x
79 - 33 = x
46 = x
Therefore, the value of CP is 46.
Given : ABCD is a rectangle and P is a point inside it such that AP = 33, BP = 16, DP = 63.
To Find : CP
Solution:
Draw 4 perpendiculars from point P on each side of rectangle
PE ⊥ AB = X
PF ⊥ BC = Y
PH ⊥ CD = Z
PG ⊥ AD = W
AP² = X² + W² = 33²
BP² = X² + Y² = 16²
CP² = Y² + Z²
DP² = W² + Z² = 63²
BP² + DP² - AP² = X² + Y² + W² + Z² - ( X² + W² )
=> BP² + DP² - AP² = Y² + Z²
=> BP² + DP² - AP² = CP²
=> 16² + 63² - 33² = CP²
=> 56² = CP²
=> CP = 56
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