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PLLEEEEASE I NEEEEED THIS

The triangular based pyramid ABCD is shown. The base ABC is right angled triangle and the pyramid has a volume of 72cm3. D is directly above A. AB=AC. AD= 2 * AB. The length AB is labelled X. Calculate x (thank you sooooo much)

User Rray
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1 Answer

5 votes

Answer:

x=6

Explanation:

It's difficult to be certain without a picture but from your description but it seems as though the base is an isosceles right triangle whose congruent sides are labeled as "x". Thus the area of the base triangle would be 1/2 x². Since AD is 2AB, the height is 2x. the volume of a pyramid is V=1/3 Bh where B is the area of the base and h is the height of the pyramid. Substituting in the given values you get the equation 72= (1/3)(1/2 x²)(2x). This simplifies to 72=1/3 x³. Multiplying both sides of the equation by 3 gives 216=x³ then taking the cube root of both sides gives x=6

User Hafez
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