+0

0
100
5
+68

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?

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?

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

Severoth  Jan 5, 2018
Sort:

#1
+5888
+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
+5888
+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
+5888
+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
+5888
+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
+5888
+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

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