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MATH / A cube has a side length of s, and its vertices are A=(0,0,0), B=(s,0,0), C=(s,s,0), D=(0,s,0), E=(0,0,s), F=(s,0,s), G=(s,s,s), and H=(0,s,s). A point P inside the cube satisfies …

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problem

A cube has a side length of s,s, and its vertices are A=(0,0,0),A = (0,0,0), B=(s,0,0),B = (s,0,0), C=(s,s,0),C = (s,s,0), D=(0,s,0),D = (0,s,0), E=(0,0,s),E = (0,0,s), F=(s,0,s),F = (s,0,s), G=(s,s,s),G = (s,s,s), and H=(0,s,s).H = (0,s,s). A point PP inside the cube satisfies PA=70,PA = \sqrt{70}, PB=97,PB = \sqrt{97}, PC=88,PC = \sqrt{88}, and PE=43.PE = \sqrt{43}. Find the side length s.s.
Plain-text mathematical notation (without MathML)
A cube has a side length of s, and its vertices are A=(0,0,0), B=(s,0,0), C=(s,s,0), D=(0,s,0), E=(0,0,s), F=(s,0,s), G=(s,s,s), and H=(0,s,s).  A point P inside the cube satisfies PA=√(70), PB=√(97), PC=√(88), and PE=√(43).  Find the side length s.
Original LaTeX notation
A cube has a side length of $s,$ and its vertices are $A = (0,0,0),$ $B = (s,0,0),$ $C = (s,s,0),$ $D = (0,s,0),$ $E = (0,0,s),$ $F = (s,0,s),$ $G = (s,s,s),$ and $H = (0,s,s).$  A point $P$ inside the cube satisfies $PA = \sqrt{70},$ $PB = \sqrt{97},$ $PC = \sqrt{88},$ and $PE = \sqrt{43}.$  Find the side length $s.$

level

Level 4

type

Precalculus

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Source and history

task_id
72007acc-f514-5d40-bc91-6b2b12d2285f
task_key
precalculus--test--72007acc-f514-5d40-bc91-6b2b12d2285f
task_revision_id
1
config / split
precalculus / test

Official source

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