The sides of a triangle are 8,15 and 18 the shortest side of a similar triangle is 10 how long are the other sides?
Find the scale factor of similar triangles whose sides are 4,12,20 and 5,15,25
Assume that traingle xyz is similar to triangle rpn with x(ray sign) r and p(ray sign) y. State three proportions that are TRUE
Prove that if one two similar triangles is isosceles, then the other is also isosceles
How to those please/
1. Triangle #1
a = 8
b = 15
c = 18
Triangle #2:
d = 10
e = ?
f = ?.
a/d = b/e = c/f = 8/10
15/e = 8/10
e = 18.75
18/f = 8/10
f = 22.5
2. Scale Factor=5/4 = 15/12=25/20 = 1.25
3. x/r = y/p = z/n.
1. 15/x = 8/10 = 18/y
15/x = 4/5; 4/5 = 18/y
4x = 75 ; 4y = 90
x= 18.75 ; y = 22.5
2. 4/5 , 12/15 , 20/25
Scale factor = 4/5 or
Perimeter ∆1/ Perimeter ∆2 = 4+12+20/5+12+25 = 36/45 = 4/5
- The ratio of the perimeter of these two triangles is equal to the scale factor.
3. X/R = Y/P = Z/N
The sides of a triangle are 8, 15, and 18. The shortest side of a similar triangle
is 10. How long are the other sides of the second triangle?
Why did the triangle go to the doctor? Because it had too many sides! But don't worry, I'm here to help you with your questions.
For the first question, we have a side length of 8 in the original triangle and a side length of 10 in the similar triangle. To find the other side lengths, we can set up a proportion:
8 / 10 = 15 / x
Now, cross-multiply and solve for x:
8x = 10 * 15
x = (10 * 15) / 8
So, the other side length in the similar triangle is approximately 18.75.
For the second question, we can find the scale factor by comparing the corresponding sides:
For the first set of sides (4, 12, 20):
scale factor = 4/5 = 12/15 = 20/25
So, the scale factor is 4/5, 12/15, or 20/25.
For the second set of sides (5, 15, 25):
scale factor = 5/4 = 15/12 = 25/20
Again, the scale factor is 5/4, 15/12, or 25/20.
For the third question, to find three proportions that are true in similar triangles XYZ and RPN, we can compare corresponding sides:
1. XY / RP = XZ / RN = YZ / PN
2. XZ / RP = YZ / RN
3. XY / XZ = RP / RN
These proportions hold true in similar triangles XYZ and RPN.
And finally, to prove that if one of two similar triangles is isosceles, then the other is also isosceles, we can use the fact that corresponding angles in similar triangles are congruent. So if one triangle has an angle that measures 90 degrees, for example, then the other triangle will also have an angle of 90 degrees. This means both triangles are isosceles.
Hope that brings some smiles to your face while tackling these questions!
To find the lengths of the other sides of a similar triangle, you can use the concept of proportionality. If the shortest side of the original triangle is 8 and the shortest side of the similar triangle is 10, you can set up a proportion using the corresponding sides of the two triangles:
8 / 15 = 10 / x
Cross-multiplying, you get:
8 * x = 15 * 10
8x = 150
x = 18.75
Therefore, the other sides of the similar triangle would be approximately 18.75 and 22.5.
To find the scale factor of similar triangles, you can compare the corresponding sides of the two triangles and determine the ratio. For the triangles with sides 4, 12, 20 and 5, 15, 25, we can take the ratio of the corresponding sides to find the scale factor:
For the first triangle:
Scale factor = 4/5 = 0.8 (approximately)
For the second triangle:
Scale factor = 12/15 = 0.8 (approximately)
For the third triangle:
Scale factor = 20/25 = 0.8 (approximately)
Therefore, the scale factor for all three similar triangles is approximately 0.8.
For triangle XYZ being similar to triangle RPN with X ~ R and P ~ Y, three true proportions can be stated:
1) XP/RY = XZ/RN
This means that the ratio of the corresponding sides XP and RY is equal to the ratio of the corresponding sides XZ and RN.
2) YP/RN = YZ/RN
This means that the ratio of the corresponding sides YP and RN is equal to the ratio of the corresponding sides YZ and RN.
3) XP/YP = XZ/YZ
This means that the ratio of the corresponding sides XP and YP is equal to the ratio of the corresponding sides XZ and YZ.
To prove that if one of two similar triangles is isosceles, then the other is also isosceles, we can use the concept of corresponding angles and ratios. Let's assume triangle ABC is similar to triangle XYZ, and triangle ABC is isosceles.
If triangle ABC is isosceles, it means that AB = AC. Since the triangles are similar, we can say corresponding sides have a ratio:
AB/XY = AC/XZ
But since AB = AC, the equation becomes:
AB/XY = AB/XZ
Dividing both sides by AB and simplifying, we get:
1/XY = 1/XZ
This implies that XY = XZ, which means triangle XYZ is isosceles as well. Therefore, if one of two similar triangles is isosceles, then the other is also isosceles.
I hope this explanation helps! Let me know if you have any further questions.