Question

Can someone please help me with number 3 and fast because is due tomorrow.

Answer 1

First, find the hypotenuse of the triangle with leg lengths 4 and 4. Use special triangle theorem:

1:1:sqrt(2) 4:4:4*sqrt(2)

Use the Pythagorean Theorem to find x:

2^2 + (4sqrt2)^2 = x^2

x^2 = 36

x = 6, or choice (D).

Answer 2

As you can tell, the shape is split into two triangles.

Solve the first triangle (which is a isosceles, as their legs are the same measurement).

An isosceles triangle's measurement angles is: 1, 1, √2

1 = 4

1 = 4

√2 = 4√2

measurement of line AC = 4√2

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Use the Pythagoream theorem: a² + b² = c² (c being the hypotenuse)

a = 2

b = 4√2

c = c

Plug into corresponding terms:

(2)² + (4√2)² = c²

Simplify

4 + (4)(4)(√2)(√2)* = c²

*Note that two of the same roots multiplied together will result in a whole number

4 + 16(2) = c²

Simplify

16 x 2 = 32

32 + 4 = 36

c² = 36

Simplify. Isolate the c. Root both sides

√c² = √36

c = √36

c = 6

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(D) 6 is your answer

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hope this helps