Mathematics
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14.07.2020

Can you please help with numbers 19-21

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06.06.2023, solved by verified expert

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**Answer:**

20) 24 cm

21) 14.7 cm

**Step-by-step explanation:**

**19. **

**
****GIVEN: **AA' = 15 units, BB' = 8 units and AB = 25 units.

**To find:** A'B'

Draw B'C = AB (ABB'C is a parallelogram)

Therefore, AC = BB' = 8 units.

CA' = 15 - 8 = 7 units.

A'CB' is a right angle traingle with B'C hypotenuse.

Using the Pythagorean theorem, we can calculate the length of the common external tangent (the side opposite to the right angle):

B'C^2 = A'B'^2 + A'C^2

25^2 = A'B'^2 + 7^2

A'B'^2 = 625 - 49 = 576

A'B' = √576 = **24 units. **

Thus, **the length of the common tanget = 24 units**

**20.**

**GIVEN: **AA' = 18 cm, BB' = 8 cm and AB = 18+8 = 26 cm.

**To find:** A'B'

Draw B'C = AB (ABB'C is a parallelogram)

Therefore, AC = BB' = 8 cm.

CA' = 18 - 8 = 10 cm.

A'CB' is a right angle traingle with B'C hypotenuse.

Using the Pythagorean theorem, we can calculate the length of the common external tangent (the side opposite to the right angle):

B'C^2 = A'B'^2 + A'C^2

26^2 = A'B'^2 + 10^2

A'B'^2 = 676 - 100 = 576

A'B' = √576 = **24 cm**

Thus, **the length of the common tanget = 24 cm**

**21.**

**GIVEN: **AA' = 9 cm, BB' =6 cm and AB = 9+6 = 15 cm.

**To find:** A'B'

Draw B'C = AB (ABB'C is a parallelogram)

Therefore, AC = BB' = 6 cm.

CA' = 9 - 6 = 3 cm.

A'CB' is a right angle traingle with B'C hypotenuse.

Using the Pythagorean theorem, we can calculate the length of the common external tangent (the side opposite to the right angle):

B'C^2 = A'B'^2 + A'C^2

15^2 = A'B'^2 + 3^2

A'B'^2 = 225 - 9 = 216

A'B' = √216 = 14.696** **cm =** 14.7 cm**

Thus, **the length of the common tanget = 14.7 cm**

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