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# 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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