Q. 294.1( 48 Votes )

# In the figure, AB

Answer :

x = 6 & y = 1

Given – in pentagon ABCDE, BE||CD and BC||DE & BC CD

AB = 5cm, AE = 5cm, BE = 7cm, BC = x-y, CD = x+y

Perimeter of ABCDE = 27 cm

To Find – values of x & y

Property – A quadrilateral with opposite sides parallel and four right angles is a rectangle.

Answer –

In quadrilateral BCDE, BE||CD and BC||DE & BC CD,

BCD = CDE = DEB = EBC = 90°

As in quadrilateral BCDE, opposite sides are parallel and all angles are right angles, hence BCDE is a rectangle.

We know that, opposite sides of rectangle are equal.

BE = CD = 7cm

x + y = 7 ………(1)

And BC = DE

BC = DE = x – y ………(2)

Now, perimeter of pentagon ABCDE is

P = AB + BC + CD + DE + EA

27 = 5 + (x – y) + 7 + (x – y) + 5

27 = 17 + 2x – 2y

10 = 2x – 2y

x – y = 5 ………(3)

Adding equations (1) & (3),

2x = 12

x = 6

Substituting x in eq (1),

6 + y = 7

y = 1

Therefore, values of x & y are 6 & 1 respectively.

OR

x & y = 1

Given equations – To Find : values of x & y

Answer –

In given equations,  Substituting and , we get,

21m + 47n = 110 ………(1)

47m + 21n = 162 ………(2)

Multiplying eq(1) by 47 and eq(2) by 21, we get,

987m + 2209n = 5170 ………(3)

987m + 441n = 3402 ………(4)

Subtracting eq(4) from eq(3),

1768n = 1768

n = 1 y = 1

Substituting n in eq(1),

21m + 47(1) = 110

21m = 110 – 47

21m = 63

m = 3  Therefore, solution for given equations is .

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