Question

Consider that A B shown on the rectangular prism measures 6 cm. What is the length of the diagonal A F?

A) 5 cm
B) 7 cm
C) 9 cm
D) 10 cm

Answer 1

B) 7 cm

Explanation:

The length of diagonal AC satisfies the relation described by the Pythagorean theorem:

AC² = AB² + BC² = (6 cm)² +(2 cm)² = 40 cm²

The length of diagonal A F also satifies the relation described by the Pythagorean theorem:

A F² = AC² +CF² = 40 cm² + (3 cm)² = 49 cm²

Then that length can be found by taking the square root of AF²:

A F = √(AF²) = √(49 cm²)

A F = 7 cm