ABCD is a parallelogram. Its diagonals AC and BD intersect at O. If AC = 16cm, and
AO = x + 2, then x=
solutions please
Answers
Answer:
We know that in a triangle the line segment joining the mid points of two sides, is parallel to the third side and measures half of the third side.
In the triangle OAB, EF is the line joining the mid points of OA and OB. Hence EF = 1/2 AB.
In the triangle OBC, FG is the line joining the midpoints of OB and OC.
hence, FG = 1/2 BC
similarly, GH = 1/2 CD and HE = 1/2 DA
perimeter of the quadrilateral EFGH = 1/2 AB + 1/2 BC + 1/2 CD + 1/2 DA
= 1/2 * perimeter of parallelogram ABCD.
The ratio = 1/2
we also note that EFGH is a parallelogram and has area 1/4 th of ABCD.
Step-by-step explanation:
The value of x is 6 cm.
Given: ABCD is a parallelogram. Its diagonals AC and BD intersect at O. If AC = 16 cm, and AO = x + 2,
To Find: The value of x.
Solution:
- We know that in a parallelogram, opposite sides are equal and parallel.
- Also, in a parallelogram, the point of intersection of the two diagonals divides the respective diagonals into two equal parts.
Coming to the numerical,
It is said that ABCD is a parallelogram. Its diagonals AC and BD intersect at O. So, from point (2) we can say that;
AO = OC = x + 2
AC = 16 cm
Now, we can frame an equation to find the value of 'x'.
AO + OC = AC
⇒ x + 2 + x + 2 = 16
⇒ 2x + 4 = 16
⇒ 2x = 16 - 4
⇒ x = 12 / 2
= 6 cm
Hence, the value of x is 6 cm.
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