Question

PLEASE HELP ME thank you

answer needs to be in simplest radical form

find d

Answer 1

ANSWER: It will be d = 10

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Answer 2

`d=10`

Explanation:

Pythagorean theorem:

`d^2+d^2=10√(2)^2,\\2d^2=200,\\d^2=100,\\d=\boxed{10}`

Alternative:

`\cos 45^(\circ)=(d)/(10√(2)),\\(√(2))/(2)=(d)/(10√(2)),\\2d=10√(2)\cdot √(2),\\2d=20,\\d=\boxed{10}`

Alternative (derived from the Pythagorean theorem):

All 45-45-90 triangles have side lengths
`x-x-x√(2)`, where
`x√(2)` is the hypotenuse. Since this triangle's hypotenuse is
`10√(2)`, its sides are
`10-10-10√(2)`.