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3 years ago

If ON= 5x - 7, LM = 4x+ 4, NM = x -7, and OL =3y-4, find the values of c and y for which LMNO MUST BE a parallelogram.

Mathematics

1 answer:

Sholpan [36]3 years ago

4 0

Answer:

x=11, y=8/3

Step-by-step explanation:

Consider quadrilateral LMNO. If this quadrilateral MUST BE a parallelogram, then

LM=NO

and

LO=MN

Thus,

$\left\{\begin{array}{l}4x+4=5x-7\\ \\x-7=3y-4\end{array}\right.$

Solve this system of two equations. From the first equation:

$4x-5x=-7-4\\ \\-x=-11\\ \\x=11$

Substitute it into the second equation:

$11-7=3y-4\\ \\3y-4=4\\ \\3y=4+4\\ \\3y=8\\ \\y=\dfrac{8}{3}$

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Norma-Jean [14]

Answer:

Base = 10 cm

Height = 60 cm

Step-by-step explanation:

The formula for the area of a triangle is $area=\frac{1}{2} *b*h$ , where b is the length of the base of the triangle, and h is the length of the height of the triangle.

We know the area is 300, and since the height of the triangle is 6 times its base, we know that $h=6*b$ . We can plug in these values into our formula for the area of a triangle, which gives us the following equation to solve:

$300=\frac{1}{2} *b*(6*b)$

$3b^2=300$

$b=\sqrt{100} =10$

The base of the triangle is 10 centimeters.

Now that we know the base of the triangle, we can plug its value in to the original formula to solve for the height of the triangle, which gives us the following equation:

$300=\frac{1}{2} *10*h$