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PSAT Math : Acute / Obtuse Triangles

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Example Question #562 : Geometry

All of the following could be the possible side lengths of a triangle EXCEPT:

Possible Answers:

6,7,9

3,4,5

2,6,7

5,7,12

5,10,14

Correct answer:

5,7,12

Explanation:

The length of the third side of a triangle must always be between (but not equal to) the sum and the difference of the other two sides.

For instance, take the example of 2, 6, and 7.

6+2=8 and 6-2=4 . Therefore, the third side length must be greater than 4 and less than 8. Because 7 is greater than 4 and less than 8, it is possible for these to be the side lengths of a triangle.

The 5, 7, 12 answer choice is the only option for which this is not the case.

7+5=12 and 7-5=2 . Therefore, the third side length must be between 2 and 12. Because it is equal to the sum, not less than the sum, it is not possible that these could be the side lengths of a triangle.

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Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar

$\text{Triangle A}$ and $\text{Triangle B}$ are similar triangles. The perimeter of Triangle A is 45” and the length of two of its sides are 15” and 10”. If the perimeter of Triangle B is 135” and what are lengths of two of its sides?

Possible Answers:

${30}''\textup{ and }{45}''$

${4}''\textup{ and }{6}''$

${13}''\textup{ and }{19}''$

${20}''\textup{ and }{30}''$

Correct answer:

${30}''\textup{ and }{45}''$

Explanation:

The perimeter is equal to the sum of the three sides. In similar triangles, each side is in proportion to its correlating side. The perimeters are also in equal proportion.

Perimeter A = 45” and perimeter B = 135”

The proportion of Perimeter A to Perimeter B is $\frac{45}{135}=\frac{1}{3}$ .

This applies to the sides of the triangle. Therefore to get the any side of Triangle B, just multiply the correlating side by 3.

15” x 3 = 45”

10” x 3 = 30“

Screen shot 2016 02 16 at 10.45.30 am

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

Find the height of a triangle if the area of the triangle = 18 and the base = 4.

Possible Answers:

Correct answer:

Explanation:

The area of a triangle = (1/2)bh where b is base and h is height. 18 = (1/2)4h which gives us 36 = 4h so h =9.

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Example Question #141 : 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 #2 : How To Find The Area Of An Acute / Obtuse Triangle

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:

$h^{2}$

$2h^{2}$

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

$3h^{2}$

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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PSAT Math : Acute / Obtuse Triangles

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #562 : Geometry

Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar

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

Example Question #141 : Geometry

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

All PSAT Math Resources

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