Line AK is perpendicular to the plane of the rectangle ABCD. Find the distance from point K to the plane of the rectangle if DC = 12cm, KB = 13cm
Since ABCD is a rectangle, AB = CD = 12 cm.
Find the distance from point K to the plane of the rectangle ABCD is AK, that is, the perpendicular.
Consider a triangle KAB: angle KAB = 90 degrees (since AK is a perpendicular), then KAB is a right-angled triangle, AB = 12 cm is a leg, KB = 13 cm is a hypotenuse (since it lies opposite a right angle). Find AK by the Pythagorean theorem:
AK = √ (KB ^ 2 – AB ^ 2);
AK = √ (13 ^ 2 – 12 ^ 2) = √ (169 – 144) = √25 = 5 (cm).
Answer: AK = 5 cm.
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