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Geometry and Measurement

SAT Right Triangles

\(\)

If \(x=70^\circ\) in the figure above, which of the following is NOT true?

(A) \(\ \ x + z = 140\)
(B) \(\ \ z + w = 90\)
(C) \(\ \ w = y = 70\)
(D) \(\ \ x + y + z = 160\)
(E) \(\ \ x + y + z + w = 180\)

A right triangle has sides \(0 < 7x < 8y < 9z.\) Which of the following is true?

(A) \(\ \ 7x + 8y = 9z\)
(B) \(\ \ 7x^2 + 8y^2= 9z^2\)
(C) \(\ \ 64y^2 - 49x^2 = 81z^2\)
(D) \(\ \ 49x^2 + 64y^2 = 81z\)
(E) \(\ \ 49x^2+64y^2 = 81z^2\)

\(\)

In the figure above, a cylinder with radius \(r\) and height \(h\) is shown. What is the volume of the cylinder if \(a=8?\)

(A) \(\ \ 4\)
(B) \(\ \ 4 \sqrt{3}\)
(C) \(\ \ 16 \pi \)
(D) \(\ \ 16 \pi \sqrt{3}\)
(E) \(\ \ 64 \pi \sqrt{3}\)

\(\)

In the figure above, \(\triangle ABC\) is a right isosceles triangle. If \(a=8,\) what is the area of a square with side length equal to \(h?\)

(A) \(\ \ \frac{8}{\sqrt{2}}\)
(B) \(\ \ 16\)
(C) \(\ \ 32\)
(D) \(\ \ 64\)
(E) \(\ \ 128\)

\(\)

If the legs of a right triangle are \(x+4\) and \(x-4\) and the hypotenuse is \(16,\) what is the value of \(x^2?\)

(A) \(\ \ 16\)
(B) \(\ \ 64\)
(C) \(\ \ 112\)
(D) \(\ \ 144\)
(E) \(\ \ 224\)

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