Given the Triangle Inequality, the amount of any two political parties of a triangle should be higher than the third side.

Given the measurements

:Therefore, this lengths cannot stand for a triangle.

Explanation:

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

You are watching: Which three lengths cannot be the lengths of the sides of a triangle?

The height,

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

**Correct answer:**

Explanation:

If

*, climate the size of must be .Using the formula for the area that a triangle (

), through , the area of the triangle must be .Explanation:

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

and are similar triangles. The perimeter that Triangle A is 45” and the size of two of that is sides space 15” and 10”. If the perimeter the Triangle B is 135” and also what space lengths of 2 of the sides?

Explanation:

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

Perimeter A = 45” and perimeter B = 135”

The proportion of Perimeter A to Perimeter B is

.This uses to the sides of the triangle. As such to obtain the any side the Triangle B, just multiply the correlating side by 3.

15” x 3 = 45”

10” x 3 = 30“

Explanation:

The sum of the lengths of 2 sides the a triangle can not be less than the size of the 3rd side. 8 + 4 = 12, i m sorry is much less than 13.

Two sides of a triangle are 20 and also 32. Which of the adhering to CANNOT be the 3rd side of this triangle.

Explanation:

Please remember the Triangle Inequality Theorem, which states that the sum of any kind of two sides of a triangle have to be better than the 3rd side. Therefore, the exactly answer is 10 since the amount of 10 and 20 would certainly not be higher than the 3rd side 32.

Explanation:

The sum of the lengths of any type of two political parties of a triangle have to exceed the size of the 3rd side; therefore, 5+7 > x, i beg your pardon cannot occur if x = 13.

The lengths of 2 sides that a triangle room 9 and 7. I m sorry of the following can be the length of the 3rd side?

Explanation:

Let us call the third side x. Follow to the Triangle Inequality Theorem, the sum of any kind of two political parties of a triangle need to be bigger than the various other two sides. Thus, all of the complying with must it is in true:

x + 7 > 9

x + 9 > 7

7 + 9 > x

We can solve these 3 inequalities to determine the possible values of x.

x + 7 > 9

Subtract 7 indigenous both sides.

x > 2

Now, we can look in ~ x + 9 > 7. Subtracting 9 from both sides, us obtain

x > –2

Finally, 7 + 9 > x, which means that 16 > x.

Therefore, x need to be better than 2, higher than –2, but additionally less 보다 16. The only number that satisfies every one of these needs is 12.

The prize is 12.

Report an Error

### Example concern #5 : just how To discover The length Of The next Of an Acute / Obtuse Triangle

The lengths the a triangle are 8, 12, and also x. I beg your pardon of the adhering to inequalities shows every one of the possible values that x?

**Possible Answers:**

4 Explanation:

According to the Triangle Inequality Theorem, the sum of any kind of two political parties of a triangle should be higher (not higher than or equal) 보다 the continuing to be side. Thus, the adhering to inequalities have to all it is in true:

x + 8 > 12

x + 12 > 8

8 + 12 > x

Let"s fix each inequality.

x + 8 > 12

Subtract 8 from both sides.

x > 4

Next, let"s look in ~ the inequality x + 12 > 8

x + 12 > 8

Subtract 12 native both sides.

See more: The Holy Spirit Cannot Dwell In An Unclean Temple Scripture, Scripture Is Clear That We Are The Temple Of God:

x > –4

Lastly, 8 + 12 > x, which means that x –4.

To summarize, x have to be higher than 4 and also less than 20. We can write this together 4 Report an Error

view SAT mathematics Tutors

Adrian Certified tutor

University that Nevada-Las Vegas, Bachelors, Mathematical sciences .

Western Governors University, Bachelor of Education, Teacher Education, multiple Levels.

New York University, Bachelors, Biochemistry.

Report an problem with this inquiry

If you"ve discovered an problem with this question, you re welcome let united state know. Through the aid of the ar we can continue to boost our educational resources.

DMCA complaint

your Infringement notice may it is in forwarded to the party that made the content obtainable or to 3rd parties such together ChillingEffects.org.

you re welcome follow these measures to document a notice:

you must include the following:

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors llc 101 S. Hanley Rd, Suite 300 St. Louis, MO 63105