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Troyanec [42]
2 years ago
5

For 4-6, determine whether the three numbers could be the lengths of the sides of a

Mathematics
1 answer:
Anika [276]2 years ago
8 0

Answer:

4. 4, 8, 11 could be the lengths of the sides of a  triangle

5. 6, 12, 5 could not be the lengths of the sides of a  triangle

6. 13, 13, 26 could not be the lengths of the sides of a  triangle

Step-by-step explanation:

There is an important rule about the sides of the triangle

  • The sum of lengths of the smallest two sides of a triangle must be greater than the length of the third side

Let us use this rule to solve questions 4, 5, and 6

#4.

∵ The numbers are 4, 8, 11

∵ The two smallest numbers are 4, 8

∵ Their sum = 4 + 8 = 12

∵ The greatest number is 11

∵ 12 > 11

∴ The sum of the two smallest number is greater than the third number

∴ The numbers could be the length of the sides of a triangle

∴ 4, 8, 11 could be the lengths of the sides of a  triangle

#5.

∵ The numbers are 6, 12, 5

∵ The two smallest numbers are 5, 6

∵ Their sum = 5 + 6 = 11

∵ The greatest number is 12

∵ 11 < 12

∴ The sum of the two smallest number is smaller than the third number

∴ The numbers could not be the length of the sides of a triangle

∴ 6, 12, 5 could not be the lengths of the sides of a  triangle

#6.

∵ The numbers are 13, 13, 26

∵ The two smallest numbers are 13, 13

∵ Their sum = 13 + 13 = 26

∵ The greatest number is 26

∵ 26 = 26

∴ The sum of the two smallest number is equal to the third number

∴ The numbers could not be the length of the sides of a triangle

∴ 13, 13, 26 could not be the lengths of the sides of a  triangle

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stira [4]

Answer:

The values of x and y are x = 3 and y = 11

Step-by-step explanation:

The isosceles triangle has two equal sides in length, and its base angles are equal in measures

In ΔJKL

∵ ΔJKL is an isosceles triangle with vertex K

→ That means the equal sides are JK and KL

∴ JK = KL

∵ JK = 8x and KL = 13x - 15

→ Equate them

∴ 13x - 15 = 8x

→ Add 15 to both sides

∵ 13x - 15 + 15 = 8x + 15

∴ 13x = 8x + 15

→ Subtract 8x from both sides

∵ 13x - 8x = 8x - 8x + 15

∴ 5x = 15

→ Divide both sides by 5 to find x

∴ x = 3

∵ K is the vertex of the ΔJKL

∴ ∠KJL and ∠KLJ are the base angles

∵ The base angles are equal in measures

∴ m∠KJL = m∠KLJ

∵ m∠KJL = 5y - 3

∴ m∠KLJ = 5y - 3

∵ The sum of the measures of the angles of a Δ is 180°

∴ m∠KJL + m∠KLJ + m∠JKL = 180°

∵ m∠JKL = 76°

→ Substitute the measures of the 3 angles in the equation

∴ 5y - 3 + 5y - 3 + 76 = 180

→ Add the like terms on the left side

∵ (5y + 5y) + (76 - 3 - 3) = 180

∴10y + 70 =180

→ Subtract 70 from both sides

∵ 10y + 70 - 70 = 180 - 70

∴ 10y = 110

→ Divide both sides by 10 to find y

∴ y = 11

∴ The values of x and y are x = 3 and y = 11

5 0
2 years ago
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