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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #13 : Isosceles Triangles

An isosceles triangle has an area of 12. If the ratio of the base to the height is 3:2, what is the length of the two equal sides?

Possible Answers:

4√3

3√3

Correct answer:

Explanation:

Area of a triangle is ½ x base x height. Since base:height = 3:2, base = 1.5 height. Area = 12 = ½ x 1.5 height x height or 24/1.5 = height². Height = 4. Base = 1.5 height = 6. Half the base and the height form the legs of a right triangle, with an equal leg of the isosceles triangle as the hypotenuse. This is a 3-4-5 right triangle.

Sat_math_167_01

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Example Question #62 : Triangles

Two sides of a triangle each have length 6. All of the following could be the length of the third side EXCEPT

Possible Answers:

Correct answer: 12

Explanation:

This question is about the Triangle Inequality, which states that in a triangle with two sides A and B, the third side must be greater than the absolute value of the difference between A and B and smaller than the sum of A and B.

Applying the Triangle Inequality to this problem, we see that the third side must be greater than the absolute value of the difference between the other two sides, which is |6-6|=0, and smaller than the sum of the two other sides, which is 6+6=12. The only answer choice that does not satisfy this range of possible values is 12 since the third side must be LESS than 12.

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Example Question #62 : Triangles

Find the area of a triangle whose base is 14in and whose height is 2ft .

Possible Answers:

$336in ^{2}$

$168in^{2}$

$196in^{2}$

$186in^{2}$

$136in^{2}$

Correct answer:

$168in^{2}$

Explanation:

This problem is solved using the geometric formula for the area of a triangle.

$A=\frac{1}{2}b*h$

Convert feet to inches.

$\dpi{100} \frac{2ft}{1}*\frac{12in}{1ft}=24in$

$A=\frac{1}{2}*14in*24in$

$A=168in^{2}$

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Example Question #335 : Plane Geometry

If triangle ABC has vertices (0, 0), (6, 0), and (2, 3) in the xy-plane, what is the area of ABC?

Possible Answers:

Correct answer:

Explanation:

Sketching ABC in the xy-plane, as pictured here, we see that it has base 6 and height 3. Since the formula for the area of a triangle is 1/2 * base * height, the area of ABC is 1/2 * 6 * 3 = 9.

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Example Question #61 : Triangles

What is the area of a triangle with a height of and a base of ?

Possible Answers:

Correct answer:

Explanation:

When searching for the area of a triangle we are looking for the amount of the space enclosed by the triangle.

The equation for area of a triangle is

Plug the values for base and height into the equation yielding

$\frac{1}{2}(4)(7)=Area$

Then multiply the numbers together to arrive at the answer .

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Example Question #871 : High School Math

The height, , of triangle PQR in the figure is one-fourth the length of . In terms of h, what is the area of triangle PQR ?

Possible Answers:

$3h^{2}$

$2h^{2}$

$h^{2}$

$\frac{1}{2}h^{2}$

Correct answer:

$2h^{2}$

Explanation:

If $\dpi{100} \small h=\frac{1}{4}$ * $\dpi{100} \small \overline{PQ}$ , then the length of $\dpi{100} \small \overline{PQ}$ must be $\dpi{100} \small 4h$ .

Using the formula for the area of a triangle ( $\frac{1}{2}bh$ ), with $\dpi{100} \small b=4h$ , the area of the triangle must be $2h^{2}$ .

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Example Question #1 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle

A triangle has a perimeter of 36 inches, and one side that is 12 inches long. The lengths of the other two sides have a ratio of 3:5. What is the length of the longest side of the triangle?

Possible Answers:

Correct answer:

Explanation:

We know that the perimeter is 36 inches, and one side is 12. This means, the sum of the lengths of the other two sides are 24. The ratio between the two sides is 3:5, giving a total of 8 parts. We divide the remaining length, 24 inches, by 8 giving us 3. This means each part is 3. We multiply this by the ratio and get 9:15, meaning the longest side is 15 inches.

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Example Question #71 : Triangles

A triangle has sides of length 8, 13, and L. Which of the following cannot equal L?

Possible Answers:

Correct answer:

Explanation:

The sum of the lengths of two sides of a triangle cannot be less than the length of the third side. 8 + 4 = 12, which is less than 13.

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Example Question #2 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle

Two sides of a triangle are 20 and 32. Which of the following CANNOT be the third side of this triangle.

Possible Answers:

Correct answer:

Explanation:

Please remember the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side. Therefore, the correct answer is 10 because the sum of 10 and 20 would not be greater than the third side 32.

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Example Question #146 : Sat Mathematics

A triangle has sides of length 5, 7, and x. Which of the following can NOT be a value of x?

Possible Answers:

Correct answer:

Explanation:

The sum of the lengths of any two sides of a triangle must exceed the length of the third side; therefore, 5+7 > x, which cannot happen if x = 13.

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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #13 : Isosceles Triangles

Example Question #62 : Triangles

Example Question #62 : Triangles

Example Question #335 : Plane Geometry

Example Question #61 : Triangles

Example Question #871 : High School Math

Example Question #1 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle

Example Question #71 : Triangles

Example Question #2 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle

Example Question #146 : Sat Mathematics

All High School Math Resources

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