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SAT Math : Geometry

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Example Questions

Example Question #25 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Given that two sides of a right triangle measure 2 feet and 3 feet, respectively, with a hypoteneuse of x, what is the perimeter of this right triangle (to the nearest tenth)?

Possible Answers:

3.6 feet

9.4 feet

8.6 feet

6.4 feet

18 feet

Correct answer:

8.6 feet

Explanation:

Using the Pythagrean Theorem, we know that $a^{2} + b^{2} = c^{2}$ $\displaystyle a^{2} + b^{2} = c^{2}$.

This tells us:

$2^{2} + 3^{2} = C^{2}$ $\displaystyle 2^{2} + 3^{2} = C^{2}$

$4 + 9 = C^{2}$ $\displaystyle 4 + 9 = C^{2}$

$13 = C^{2}$ $\displaystyle 13 = C^{2}$

Taking the square root of both sides, we find that C = 3.6 $\displaystyle C = 3.6$

To find the perimeter, we add the side lengths together, which gives us that the perimeter is: $\displaystyle 3 + 2 + 3.6 = 8.6$

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Example Question #26 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

$In\;\Delta GHJ, \;what\;is\;the\;length\;of\;\overline{GJ}?$ $\displaystyle In\;\Delta GHJ, \;what\;is\;the\;length\;of\;\overline{GJ}?$

Possible Answers:

$\displaystyle 13$

$\displaystyle 5$

$\displaystyle 10$

$\displaystyle 12$

Correct answer:

$\displaystyle 13$

Explanation:

$Use\;the\;Pythagorean\;Theorem:A^2+B^2=C^2,\;to\; find\;\overline{GJ}.$ $\displaystyle Use\;the\;Pythagorean\;Theorem:A^2+B^2=C^2,\;to\; find\;\overline{GJ}.$

$\displaystyle 5^2+12^2=C^2$

$\displaystyle 25+144=C^2$

169=C^2 $\displaystyle 169=C^2$

$C=\sqrt{169}=13$ $\displaystyle C=\sqrt{169}=13$

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Example Question #41 : Right Triangles

Kathy and Jill are travelling from their home to the same destination. Kathy travels due east and then after travelling 6 miles turns and travels 8 miles due north. Jill travels directly from her home to the destination. How miles does Jill travel?

Possible Answers:

$\dpi{100} \small 14\ miles$ $\displaystyle \dpi{100} \small 14\ miles$

$\dpi{100} \small 10\ miles$ $\displaystyle \dpi{100} \small 10\ miles$

$\dpi{100} \small 16\ miles$ $\displaystyle \dpi{100} \small 16\ miles$

$\dpi{100} \small 12\ miles$ $\displaystyle \dpi{100} \small 12\ miles$

$\dpi{100} \small 8\ miles$ $\displaystyle \dpi{100} \small 8\ miles$

Correct answer:

$\dpi{100} \small 10\ miles$ $\displaystyle \dpi{100} \small 10\ miles$

Explanation:

Kathy's path traces the outline of a right triangle with legs of 6 and 8. By using the Pythagorean Theorem

$\dpi{100} \small 6^{2}+8^{2}=x^{2}$ $\displaystyle \dpi{100} \small 6^{2}+8^{2}=x^{2}$

$\dpi{100} \small 36+64=x^{2}$ $\displaystyle \dpi{100} \small 36+64=x^{2}$

$\dpi{100} \small x=10$ $\displaystyle \dpi{100} \small x=10$ miles

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Example Question #411 : Plane Geometry

$Which\; of \;the \;following \;is\; NOT\; true\; about \;the \;hypotenuse \;of \;a\; triangle?$ $\displaystyle Which\; of \;the \;following \;is\; NOT\; true\; about \;the \;hypotenuse \;of \;a\; triangle?$

Possible Answers:

$It\;is\;always\;across\;from\;the\;largest\;angle\;in\;the\;triangle.$ $\displaystyle It\;is\;always\;across\;from\;the\;largest\;angle\;in\;the\;triangle.$

$It\;is\;the\;longest\;side.$ $\displaystyle It\;is\;the\;longest\;side.$

$It\;is\;always\;greater\;than\;1.$ $\displaystyle It\;is\;always\;greater\;than\;1.$

$It\;is\;across\;from\;the\;right\;angle.$ $\displaystyle It\;is\;across\;from\;the\;right\;angle.$

Correct answer:

$It\;is\;always\;greater\;than\;1.$ $\displaystyle It\;is\;always\;greater\;than\;1.$

Explanation:

$The\;hypotenuse\;can\;be\;between\;0\;and\;1.$ $\displaystyle The\;hypotenuse\;can\;be\;between\;0\;and\;1.$

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Example Question #61 : Triangles

In order to get to work, Jeff leaves home and drives 4 miles due north, then 3 miles due east, followed by 6 miles due north and, finally, 7 miles due east. What is the straight line distance from Jeff’s work to his home?

Possible Answers:

10√2

2√5

6√2

Correct answer:

10√2

Explanation:

Jeff drives a total of 10 miles north and 10 miles east. Using the Pythagorean theorem (a²+b²=c²), the direct route from Jeff’s home to his work can be calculated. 10²+10²=c². 200=c². √200=c. √100√2=c. 10√2=c

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Example Question #62 : Triangles

Jim leaves his home and walks 10 minutes due west and 5 minutes due south. If Jim could walk a straight line from his current position back to his house, how far, in minutes, is Jim from home?

Possible Answers:

√10

5√5

6√6

√5

Correct answer:

5√5

Explanation:

By using Pythagorean Theorem, we can solve for the distance “as the crow flies” from Jim to his home:

10² + 5² = x²

100 + 25 = x²

√125 = x, but we still need to factor the square root

√125 = √25*5, and since the √25 = 5, we can move that outside of the radical, so

5√5= x

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Example Question #61 : Triangles

A square enclosure has a total area of 3,600 square feet. What is the length, in feet, of a diagonal across the field rounded to the nearest whole number?

Possible Answers:

100

Correct answer:

Explanation:

In order to find the length of the diagonal accross a square, we must first find the lengths of the individual sides.

The area of a square is found by multiply the lengths of 2 sides of a square by itself.

So, the square root of 3,600 comes out to 60 ft.

The diagonal of a square can be found by treating it like a right triangle, and so, we can use the pythagorean theorem for a right triangle.

60² + 60² = C²

the square root of 7,200 is 84.8, which can be rounded to 85

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Example Question #51 : Triangles

Triangle

If the length of CB is 6 and the angle C measures 45º, what is the length of AC in the given right triangle?

Possible Answers:

6√2

12√2

Correct answer:

6√2

Explanation:

Pythagorean Theorum

AB² + BC² = AC²

If C is 45º then A is 45º, therefore AB = BC

AB² + BC² = AC²

6² + 6² = AC²

2*6² = AC²

AC = √(2*6²) = 6√2

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Example Question #491 : Geometry

You leave on a road trip driving due North from Savannah, Georgia, at 8am. You drive for 5 hours at 60mph and then head due East for 2 hours at 50mph. After those 7 hours, how far are you Northeast from Savannah as the crow flies (in miles)?

Possible Answers:

$\sqrt{10000}$ $\displaystyle \sqrt{10000}$

$\sqrt{90000}$ $\displaystyle \sqrt{90000}$

$\sqrt{80000}$ $\displaystyle \sqrt{80000}$

$\sqrt{70000}$ $\displaystyle \sqrt{70000}$

$\sqrt{100000}$ $\displaystyle \sqrt{100000}$

Correct answer:

$\sqrt{100000}$ $\displaystyle \sqrt{100000}$

Explanation:

Distance = hours * mph

North Distance = 5 hours * 60 mph = 300 miles

East Distance = 2 hours * 50 mph = 100 miles

Use Pythagorean Theorem to determine Northeast Distance

300^{2 +}100²=NE²

90000 + 10000 = 100000 = NE²

NE = √100000

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Example Question #63 : Triangles

A square garden has an area of 49 ft². To the nearest foot, what is the diagonal distance across the garden?

Possible Answers:

Correct answer:

Explanation:

Since the garden is square, the two sides are equal to the square root of the area, making each side 7 feet. Then, using the Pythagorean Theorem, set up the equation 7²+ 7²= the length of the diagonal squared. The length of the diagonal is the square root of 98, which is closest to 10.

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SAT Math : Geometry

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #25 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #26 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #41 : Right Triangles

Example Question #411 : Plane Geometry

Example Question #61 : Triangles

Example Question #62 : Triangles

Example Question #61 : Triangles

Example Question #51 : Triangles

Example Question #491 : Geometry

Example Question #63 : Triangles

All SAT Math Resources

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