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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