Question

∆KLM, KL=LM, периметр KLM =138, биссиктриса LQ= 42. Найти периметр KLQ

Answer 1

Ответ: 111

Объяснение:

L-вершина, KM-основание,    KL=LM=a,  KM=b,   KQ=QM=b/2, т.к. биссектр. равноб. тр-ка явл и медианой, 2a+b=138(по усл),  а+b/2=138/2=69, P(KLQ)=a+b/2+LQ=69+42=111

Answer 2

To find the perimeter of KLQ, we need to determine the lengths of KL, LM, and LQ. Let's use the information provided in the problem to calculate these values step by step:

Given:

• KL = LM
• Perimeter of ∆KLM = 138
• Length of the bisector LQ = 42

Step 1: Perimeter of ∆KLM Since KL = LM, let's denote KL = LM = x. The perimeter of ∆KLM is the sum of the three sides: KL + LM + KM. In this case, it's 2x + KM (since KL = LM = x).

Step 2: Determine KM To find KM, we know that the perimeter of ∆KLM is 138, so we have the equation: 2x + KM = 138

Step 3: Determine LQ and KQ Since LQ is the bisector of angle KLM, we can split the side KM into two parts: KQ and QM, where KQ = QM. So, KM = KQ + QM = KQ + LQ.

Step 4: Substitute LQ in the equation From Step 3, we know that KM = KQ + LQ, so we can replace KM with KQ + LQ in the equation from Step 2: 2x + (KQ + LQ) = 138

Step 5: Find KQ Now, we need to find KQ. Since KQ = QM, we have KQ = QM = LQ/2 = 42/2 = 21.

Step 6: Substitute KQ in the equation Now, let's replace KQ with 21 in the equation: 2x + (21 + LQ) = 138

Step 7: Solve for LQ To find LQ, we can simplify the equation: 2x + 21 + LQ = 138 LQ = 138 - 2x - 21 LQ = 117 - 2x

Step 8: Find x At this point, we need another piece of information to find the value of x. The problem statement doesn't provide enough details to determine the specific value of x.

However, if you have additional information about the relationship between KL and LM or any other relevant details, please provide it, and I'll be happy to assist you further in finding the perimeter of KLQ.