Given: KLMN is a trapezoid, KF =10 MF ║ LK AKLMF = AFMN Find: KN
1 answer:
You can see the trapezoid in the attached picture.
The data given in the problem are:
KF = 10
LK // MF
A(KLMF) = A(FMN)
We know that KLMF is a parallelogram because:
LM // KF (bases of the trapezoid)
LK // MF (hypothesis).
The area of a parallelogram is given by the formula:
A(KLMF) = b × h
= KF <span>× h</span>
= 10 × h
The area of a triangle is given by the formula:
<span>A(FMN) = (b × h) / 2
= (FN </span>× h) / 2
The problem states that the two areas are congruent, therefore:
A(KLMF) = <span>A(FMN)
</span>10 × h = FN <span>× h / 2
10 = FN </span><span>/ 2
FN = 20
Therefore we can calculate:
KN = KF + FN = 10 + 20 = 30
Hence, KN is 30 units long.</span>
The data given in the problem are:
KF = 10
LK // MF
A(KLMF) = A(FMN)
We know that KLMF is a parallelogram because:
LM // KF (bases of the trapezoid)
LK // MF (hypothesis).
The area of a parallelogram is given by the formula:
A(KLMF) = b × h
= KF <span>× h</span>
= 10 × h
The area of a triangle is given by the formula:
<span>A(FMN) = (b × h) / 2
= (FN </span>× h) / 2
The problem states that the two areas are congruent, therefore:
A(KLMF) = <span>A(FMN)
</span>10 × h = FN <span>× h / 2
10 = FN </span><span>/ 2
FN = 20
Therefore we can calculate:
KN = KF + FN = 10 + 20 = 30
Hence, KN is 30 units long.</span>
You might be interested in
Answer:
the second number line in the second row OR The number line D in the attached image
Step-by-step explanation:
Lets start solving the question.
(For ease of understanding each line i have labeled them please see the attachment to relate my explanation)
first read the question it i mentioned that which number line currently shows 0.8+0.3.
After reading the question it is clear that which ever line will represent it will be the addition of 08.+0.3.
here please take a note that we are dealing with a number line hence the sign also matters.
Now lets start analyzing lines one by one.To make it easy i have attached an image where i have labeled the lines as A,B,C,D,E,and F for the ease of understanding.
so take the first line A into consideration,
its starting from 0.3 and ending at 0 means its decrementing you can also determine it with the direction. any line that originates from the origin and goes to the right shows increment and addition and the lines that originates from origin and goes to the left shows decrement.
so here we can easily all those lines which are showing a leftward directions as it is decrementing and we want a line that increments 0.8+0.3
so now th lines A,B,F and H can be skipped.
We are done with analyzing line A, line B is skipped and now lets start with C.
here the line start from 0 and ends at 0.8 so it cant be the line as 0.8+0.3 yields 0.11.
so line C can't be the correct one.
Now lets consider the next line that is D.
here it starts at 0.8 and ends at 0.11 means exactly showing an increment of 0.3 also its showing a positive directions as its heading to the right.
so this is the line that correctly shows 0.8+0.3.
Now consider line E it cant be the correct line as its showing only 0 to 0.8.
and now the line that will confuse you is line G.
it starts at 0.3 and ends at 0.11 here there is increment of 0.8 though it seems like correct but it cant be the line showing 0.8+0.3 as we have to select the line that originates at 0.8 and shows an increment of 0.3 and not the one which originates at 0.3 and ends at 0.11 showing an increment of 0.8.
Also the question itself is asking 'LINE' and not 'LINES' so you can take such minute things also into Consideration for avoiding any kind of confusion.
I hope this will help you.
