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balu736 [363]
2 years ago
15

During gym class, Lenny, Lonnie, and Lainey measure the length of their long jumps. Lenny’s jump is ⅔ times the length of Lainey

’s, and Lonnie’s jump is 1⅓ times the length of Lainey’s. Whose jump is the longest? Why? pls help!!
Mathematics
1 answer:
Svetllana [295]2 years ago
3 0

Answer: Lonnie’s Jump

Step-by-step explanation:

         (They just <em>had</em> to give three names that all started with L.)

         Since Lenny's jump is ⅔ times the length of Lainey’s, we can tell that Lenny's jump won't be the longest because it is already smaller than Lainey's.

         Since Lenny is now out of the picture, let us look at Lonnie and Lainey. Lonnie’s jump is 1 ⅓ times the length of Lainey’s. Since Lonnie's jump is longer than Laniey's, Lonnie's jump is the longest jump.

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PQ and QR are two sides of a regular 12-sided polygon. PR is the diagonal of the polygon.
skelet666 [1.2K]

The size of angle PRQ is 15°

Step-by-step explanation:

In any regular polygon of n-sided

  • All sides are equal in length
  • All angles are equal in measure
  • The measure of each interior angle is \frac{(n-2)*180}{n}
  • The measure of each exterior angle is \frac{360}{n}
  • The sum of the measures of the interior and exterior angle at the same vertex is 180°

∵ PQ and QR are two sides of a regular 12-sided polygon

∴ PQ = QR

∵ PR is a diagonal

∴ ∠PQR is an interior angle of the polygon

- By using the rule of the interior angle above

∵ n = 12

∴ m∠PQR = \frac{(12-2)*180}{12}

∴ m∠PQR = 150°

In Δ PQR

∵ PQ = QR ⇒ sides in a regular polygon

- Δ PQR is an isosceles Δ

∴ m∠PRQ = m∠RPQ ⇒ base angles of an isosceles Δ

The sum of the measures of the interior angles of a triangle is 180°

∵ m∠PQR + m∠PRQ + m∠RPQ = 180°

∴ 150 + m∠PRQ + m∠RPQ = 180°

- Subtract 150 from both sides

∴ m∠PRQ + m∠RPQ = 30

∵ m∠PRQ = m∠RPQ

- Divide their sum by 2 to find the measure of each one

∴ m∠PRQ = m∠RPQ = 30 ÷ 2 = 15°

∴ m∠PRQ = 15°

The size of angle PRQ is 15°

Learn more:

You can learn more about the triangles in brainly.com/question/3945600

#LearnwithBrainly

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