If triangle DEF similar to triangle KLM such that DE=(2x+2)cm,DF=(5x-7)cm,KL=2cm,KM=3cm and EF=10cm,find the LM.
DE/KL = DF/KM = EF/LM
(2x+2)/2 = (5x-7)/3
6x+6 = 10x-14
x = 5
10/LM = x+1 = 6
LM = 5/3
Thank you
LM=5/3
LM=5/3
LM 5/3c.m
Why did the triangle go to the comedy club?
To catch a tangential line!
Now, let's solve your problem. Since triangle DEF is similar to triangle KLM, we can set up a proportion:
(DE / KL) = (EF / LM)
Replacing the given values:
((2x + 2) / 2) = (10 / LM)
Cross-multiplying:
(2x + 2) * LM = 2 * 10
Simplifying:
2x * LM + 2 * LM = 20
Dividing both sides by 2:
x * LM + LM = 10
Factoring out LM:
LM * (x + 1) = 10
Dividing both sides by (x + 1):
LM = 10 / (x + 1)
And there you have it! LM is equal to 10 divided by the sum of x and 1.
To find the length of segment LM, we first need to determine the value of x using the given information and solve for it.
Since triangle DEF is similar to triangle KLM, we can set up a proportion using the corresponding side lengths:
DE / KL = EF / LM
Substituting the given values:
(2x+2) / 2 = 10 / LM
To solve for x, we can cross-multiply:
10(2x+2) = 2 * LM
Simplifying the equation:
20x + 20 = 2 * LM
Next, we'll find the length of segment LM by plugging in the given values of KL = 2cm, KM = 3cm, and EF = 10cm.
Substituting these values into the equation, we have:
20x + 20 = 2 * 3
20x + 20 = 6
Subtracting 20 from both sides:
20x = 6 - 20
20x = -14
Dividing both sides by 20:
x = -14 / 20
Simplifying:
x = -7 / 10
Now we need to find the length of LM. Plugging in the value of x into one of the original given equations involving LM, let's use the proportion:
DE / KL = EF / LM
(2x+2) / 2 = 10 / LM
Substituting x = -7 / 10:
(2(-7/10) + 2) / 2 = 10 / LM
(-14/10 + 2) / 2 = 10 / LM
Simplifying the numerator:
(-14 + 20) / 10 = 10 / LM
6 / 10 = 10 / LM
Cross-multiplying:
6 * LM = 10 * 10
6 * LM = 100
Dividing both sides by 6:
LM = 100 / 6
Simplifying:
LM ≈ 16.67 cm
Therefore, the length of LM is approximately 16.67 centimeters.