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

Answer:

$d=10$

Step-by-step explanation:

Pythagorean theorem:

$d^2+d^2=10\sqrt{2}^2,\\2d^2=200,\\d^2=100,\\d=\boxed{10}$

Alternative:

$\cos 45^{\circ}=\frac{d}{10\sqrt{2}},\\\frac{\sqrt{2}}{2}=\frac{d}{10\sqrt{2}},\\2d=10\sqrt{2}\cdot \sqrt{2},\\2d=20,\\d=\boxed{10}$

Alternative (derived from the Pythagorean theorem):

All 45-45-90 triangles have side lengths $x-x-x\sqrt{2}$, where $x\sqrt{2}$ is the hypotenuse. Since this triangle's hypotenuse is $10\sqrt{2}$, its sides are $10-10-10\sqrt{2}$.