Q. 13. If the diagonals of a
parallelogram are x+y = 16 and
Y+7= 20 then value of x and y
are
Answers
Answered by
22
✬ x = 3 ✬
✬ y = 13 ✬
Step-by-step explanation:
Given:
- Diagonals of parallelogram are x + y = 16 and y + 7 = 20
To Find:
- What is the value of x and y ?
Solution: Let ABCD be a parallelogram where
- AC and BD = Diagonals
Let the both diagonal bisect each other point O such that AO = OC & DO = OB
- AO = 16
- OC = x + y
- DO = 20
- OB = y + 7
➟ DO = OB
➟ 20 = y + 7
➟ 20 – 7 = y
➟ 13 = y....(1)
And also
➟ AO = OC
➟ 16 = x + y
➟ 16 = x + 13 (from equation 1)
➟ 16 – 13 = x
➟ 3 = x
Hence, the values of x and y is 3 and 13 respectively.
_______________
★ Verification ★
➭ x + y = 16
➭ 3 + 13 = 16
➭ 16 = 16
➭ y + 7 = 20
➭ 13 + 7 = 20
➭ 20 = 20
Attachments:
Answered by
24
✒ Given :-
- Diagonals of a Parallelogram :- x+y = 16 and y+7 = 20.
✒ To Find :-
- The Value Of X and Y.
✒ Solution :-
⭐ Let,
The Equation x+y = 16 be Equation 1.
The Equation y+7 = 20 be Equation 2.
Now,
First, Take The Equation 2 :-
➠ y+7 = 20.
Use Transposition.
➠ y = 20-7
Subtract them.
➠ y = 13.
So, The Value Of Y = 13.
Now,
Put the value of Y in Equation 1 :-
➠ x+y = 16.
➠ x+13 = 16.
Use Transposition.
➠ x = 16-13
Subtract them.
➠ x = 3.
So, The Values Of X and Y are 3 and 13 respectively.
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