MO Z8–I–6 2018

The KLMN trapezium, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line.

Correct answer:

x =  28 cm

Step-by-step explanation:

$$\begin{gathered} k=40\text{cm} \\ m=16\text{cm} \\ S=\frac{k+m}{2}\cdot h \\ {S}_1=\frac{x\cdot h}{2} \\ {S}_1=\frac{S}{2} \\ \frac{x\cdot h}{2}=\frac{k+m}{4}\cdot h \\ 2\cdot x\cdot h=(k+m)\cdot h \\ x=(k+m)/2=(40+16)/2=28\text{cm} \end{gathered}$$

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