+0  
 
0
1069
5
avatar+110 

The triangles are similar.
 

What is the value of x?

https://static.k12.com/nextgen_media/assets/1544620-IM2_141011_020901.jpg

 

 

The triangles are similar.
 

What is the value of x?

https://static.k12.com/nextgen_media/assets/1544628-IM2_141011_020906.jpg

 

What is ED?

https://static.k12.com/nextgen_media/assets/8103943-NG_GMT_DP024_319_002.jpg

 

Hunter designs two flags for his adventure club.

What is the length of the base, x, of the larger flag?

Enter your answer, as a decimal, in the box.

https://static.k12.com/nextgen_media/assets/8103945-NG_GMT_DP024_320_001.jpg

 

A hockey player passes a puck to his teammate by bouncing it off a wall. The angles formed when the puck hits the wall and bounces off are congruent. Some of the distances are shown.

What is the distance, x,  from Player 1 to the wall?

Enter your answer, as a decimal, in the box. Round your answer to the nearest hundredth.

https://static.k12.com/nextgen_media/assets/8103948-NG_GMT_DP024_321_001.jpg

Severoth  Jan 5, 2018
 #1
avatar+7336 
+2

The triangles are similar:

 

What is the value of  x  ?

Notice that...

 

3 * 4  =  12

5 * 4  =  20

 

To make the bigger triangle, take each side of the smaller triangle and multiply it by  4  .

 

So...to find  x  ,  take the corresponding side on the smaller triangle and multiply it by  4 .

hectictar  Jan 5, 2018
 #2
avatar+7336 
+2

The triangles are similar.

What is the value of  x  ?

Like the last problem, notice...

 

7 * 4  =  28

24 * 4  =  96

 

each side of the bigger triangle   =   4 * the corresponding side of the smaller triangle

 

25 * 4   =   6x + 28

100   =   6x + 28       Subtract  28  from both sides.

72   =   6x                 Divide both sides by  6 .

12   =   x

hectictar  Jan 5, 2018
 #3
avatar+7336 
+2

What is ED ?

 

m∠AEB  =  m∠DEC   because they are vertical angles.

m∠EBA  =  m∠ECD   because they are alternate interior angles.

 

Therefore  △AEB ~ △DEC  by  AA similarity.  And...

 

AB / CD   =   AE / ED

9 / 6   =   (2x + 4) / (x + 4)     Cross multiply.

9(x + 4)   =   6(2x + 4)

9x + 36  =   12x + 24           Subtract  9x  and  24  from both sides.

36 - 24   =   12x - 9x

12   =   3x                    Divide both sides by  3 .

4   =   x

 

And...          ED   =   x + 4   =   4 + 4   =   8

hectictar  Jan 5, 2018
 #4
avatar+7336 
+2

Hunter designs two flags for his adventure club.  What is the length of the base, x, of the larger flag?

 

 

 

These two triangles are similar by  AA similarity, so...

 

5/4   =   x/5         Multiply both sides of the equation by  5 .

25/4   =   x

6.25   =   x

hectictar  Jan 6, 2018
 #5
avatar+7336 
+2

A hockey player passes a puck to his teammate by bouncing it off a wall. The angles formed when the puck hits the wall and bounces off are congruent. Some of the distances are shown.  What is the distance, x,  from Player 1 to the wall?

 

 

These two triangles are similar by  AA similarity.

 

12 / 9   =   x / 8            Multiply both sides by  8 .

96 / 9   =   x

10.67   ≈   x

hectictar  Jan 6, 2018

16 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.