contestada

3. Given quad GHJK is a trapezoid. PQ is the
median.
H
P
Q
G
K
a. If HJ = 40 and PQ=28, find GK.
b. If HJ = 5x, PQ = 5x - 9, and GK = 3x + 2,
then solve for x.
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3 Given quad GHJK is a trapezoid PQ is the median H P Q G K a If HJ 40 and PQ28 find GK b If HJ 5x PQ 5x 9 and GK 3x 2 then solve for x class=

Respuesta :

akposevictor

Applying the Trapezoid Midsegment Theorem, a. GK = 16 b. x = 10

What is the Trapezoid Midsegment Theorem?

  • Based on the Trapezoid Midsegment Theorem, the midsegment of a trapezium is parallel to the bases of the trapezium.
  • Based on the theorem, the length of the midsegment of the trapezium is half the sum of the two bases.

a. HJ = 40

PQ = 28

  • Thus:

PQ = 1/2(HJ + GK)

  • Substitute

28 = 1/2(40 + GK)

  • Solve for GK

56 = 40 + GK

GK = 56 - 40

GK = 16

b. HJ = 5x

PQ = 5x - 9

GK = 3x + 2

  • Thus:

PQ = 1/2(HJ + GK)

  • Substitute

5x - 9 = 1/2(5x + 3x + 2)

  • Solve for x

2(5x - 9) = 8x + 2

10x - 18 = 8x + 2

10x - 8x = 18 + 2

2x = 20

x = 10

In summary, applying the Trapezoid Midsegment Theorem, a. GK = 16 b. x = 10

Learn more about the Trapezoid Midsegment Theorem on:

https://brainly.com/question/4451516

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