Question

The sides of a rectangle are 19 units,10 units, 2x - y and - x + 2y units,then the values of x, y and x + y are​

Answer 1

Answer:

the opposite sides of a rectangle are equal

so,

2x-y=19

=> y=2x-19

again,

-x+2y=10

=> -x+2(2x-19)=10

=> -x+4x-38=10

=> 3x=10+38

=> 3x=48

=> x=48/3

=> x=16

y=2x-19=2.16-19=32-19=13

so, x=16, y=13 and x+y=16+13=29

Answer 2

Given :- The sides of a rectangle are 19 units,10 units, 2x - y and - x + 2y units .

To Find :- the values of x, y and x + y ?

Concept used :-

• Opposite sides of rectangle are equal in measure .

Solution :-

Since opposite sides are equal .

→ 2x - y = 19 ------- Eqn.(1)

→ 2y - x = 10 ------- Eqn.(2)

adding Eqn.(1) and Eqn.(2),

→ (2x - y) + (2y - x) = 19 + 10

→ 2x - x + 2y - y = 29

→ x + y = 29 (Ans.) ---------- Eqn.(3)

subtracting Eqn.(2) from Eqn.(1) ,

→ (2x - y) - (2y - x) = 19 - 10

→ 2x + x - y - 2y = 9

→ 3x - 3y = 9

→ 3(x - y) = 9

→ x - y = 3 ----------- Eqn.(4)

now, adding Eqn.(3) and Eqn.(4)

→ (x + y) + (x - y) = 29 + 3

→ x + x + y - y = 32

→ 2x = 32

→ x = 16 (Ans.)

putting value of x in Eqn.(1)

→ 16 + y = 29

→ y = 29 - 16

→ y = 13 (Ans.)

Hence, the values of x, y and x + y are 16, 13 and 29 respectively .

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