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## GMAT - Problem Solving - Geometry

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### A rectangular box is 10 inches wide, 10 inches long, and 5 inches high. What is the greatest possible (straight-line) distance, in inches, between any two points on the box?

A rectangular box is 10 inches wide, 10 inches long, and 5 inches high. What is the greatest possible (straight-line) distance, in inches, between any two points on the box?

Greatest possible distance between two points = distance between two opposite vertices = length of body diagonal

$\sqrt { { length }^{ 2 }+{ width }^{ 2 }+{ height }^{ 2 } }$

$\sqrt { { 10 }^{ 2 }+{ 10 }^{ 2 }+{ 5 }^{ 2 } } =\sqrt { 225 } =\quad 15$

Greatest possible distance between two points = distance between two opposite vertices = length of body diagonal

$\sqrt { { length }^{ 2 }+{ width }^{ 2 }+{ height }^{ 2 } }$

$\sqrt { { 10 }^{ 2 }+{ 10 }^{ 2 }+{ 5 }^{ 2 } } =\sqrt { 225 } =\quad 15$