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**+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**+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**+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**+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**+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