Find the value of w

Leave answer in surd form

w =

Step-by-step explanation:

Applying 3 applications of Pythagoras' identity on the 3 right triangles from left to right.

Left right triangle ( finding vertical side v ), then

v² + 7² = 9²

v² + 49 = 81 ( subtract 49 from both sides )

v² = 32 ( take the square root of both sides )

v = = 4

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Middle right triangle ( finding hypotenuse h ), then

h² = 5² + v² = 5² + (4 )² = 25 + 32 = 57 ( square root of both sides )

h =

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Right side right triangle ( finding hypotenuse w ), then

w² = 4² + h² = 4² + ( )² = 16 + 57 = 73 ( square root of both sides )

w =

d

step-by-step explanation:

step-by-step explanation: