How To Find The Third Side Of An Obtuse Triangle

All High School Math Resource

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

Explanation:

We know that the perimeter is 36 inches, and 1 side is 12. This ways, the sum of the lengths of the other ii sides are 24. The ratio between the two sides is three:v, giving a total of eight parts. We divide the remaining length, 24 inches, by 8 giving us iii. This means each office is three. We multiply this by the ratio and get 9:fifteen, meaning the longest side is 15 inches.

A triangle has sides of length eight, 13, and L. Which of the post-obit cannot equal L?

Caption:

The sum of the lengths of 2 sides of a triangle cannot be less than the length of the third side. 8 + 4 = 12, which is less than 13.

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

Explanation:

Delight remember the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must exist greater than the third side. Therefore, the correct answer is 10 because the sum of 10 and xx would non be greater than the tertiary side 32.

A triangle has sides of length v, seven, and ten. Which of the post-obit tin Non be a value of x?

Explanation:

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

The lengths of 2 sides of a triangle are 9 and 7. Which of the following could be the length of the tertiary side?

Explanation:

Allow u.s. phone call the tertiary side x. Co-ordinate to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be larger than the other ii sides. Thus, all of the following must be truthful:

x + 7 > ix

ten + 9 > 7

7 + 9 > x

Nosotros can solve these iii inequalities to decide the possible values of x.

10 + 7 > 9

Subtract 7 from both sides.

x > 2

Now, we tin can await at 10 + 9 > 7. Subtracting 9 from both sides, nosotros obtain

x > –2

Finally, 7 + ix > x, which means that sixteen > x.

Therefore, x must be greater than 2, greater than –2, only besides less than 16. The only number that satisfies all of these requirements is 12.

The answer is 12.

The lengths of a triangle are eight, 12, and x. Which of the post-obit inequalities shows all of the possible values of x?

Possible Answers:

iv ≤ x ≤ 20

viii < x < 12

4 ≤ x ≤12

4 < 10 < 20

4 < x <12

Correct answer:

4 < x < xx

Explanation:

According to the Triangle Inequality Theorem, the sum of any ii sides of a triangle must exist greater (not greater than or equal) than the remaining side. Thus, the post-obit inequalities must all exist true:

ten + 8 > 12

x + 12 > 8

8 + 12 > x

Let'south solve each inequality.

x + 8 > 12

Subtract 8 from both sides.

x > 4

Side by side, let's look at the inequality x + 12 > eight

10 + 12 > viii

Decrease 12 from both sides.

10 > –four

Lastly, 8 + 12 > x, which ways that 10 < xx.

This means that ten must be less than twenty, but greater than 4 and greater than –iv. Since any number greater than iv is besides greater than –iv, nosotros tin can exclude the inequality x > –4.

To summarize, 10 must exist greater than iv and less than 20. We tin write this as 4 < x < 20.

The answer is four < x < 20.

If 2 sides of the triangle are accept lengths equal to 8 and 14, what is i possible length of the third side?

Possible Answers:

Not plenty information

Explanation:

The sum of the lengths of 2 sides of a triangle must be greater than—but non equal to—the length of the 3rd side. Farther, the third side must be longer than the divergence between the greater and the lesser of the other two sides; therefore, xx is the only possible respond.

$4+viii< 14$

$6+8= 14$

$8+14> 20$

$8+14=22$

In $\Delta ABC$ the length of AB is fifteen and the length of side Air-conditioning is 5. What is the to the lowest degree possible integer length of side BC?

Explanation:

Rule - the length of ane side of a triangle must be greater than the differnce and less than the sum of the lengths of the other two sides.

Given lengths of two of the sides of the $\Delta ABC$ are 15 and 5. The length of the third side must be greater than 15-5 or 10 and less than 15+5 or 20.

The question asks what is the to the lowest degree possible integer length of BC, which would be 11

Two sides of a triangle have lengths iv and 7. Which of the following represents the set up of all possible lengths of the third side, 10?

Possible Answers:

4 < x < 7

2 < x < 12

4 < x < 11

three < ten < vii

three < x < eleven

Correct answer:

three < x < xi

Caption:

The set of possible lengths is: 7-4 < x < 7+4, or three < X < xi.

If two sides of a triangle take lengths 8 and 10, what could the length of the third side Non be?

Explanation:

According to the Triangle Inequality Theorem, the sums of the lengths of whatever two sides of a triangle must be greater than the length of the tertiary side. Since ten + eight is xviii, the only length out of the reply choices that is not possible is 19.

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