Question

Using information given in the following figure, find the length and breadth of this rectangle in cm.

Answer 1

The opposite sides of a rectangle are of equal lengths.

∴ 5m + n = 2m + 3n + 5

∴ 5m − 2m + n − 3n = 5

∴ 3m − 2n = 5    ...(1)

Also, 3m − 2n + 7 = m + n − 3

∴ 3m − m − 2n − n = − 3 − 7

∴ 2m − 3n = − 10    ...(2)

Multiplying equation (1) by 3 and equation (2) by 2,

9m − 6n = 15    ...(3) and

4m − 6n = − 20    ...(4)

Subtracting equation (4) from equation (3),

9m − 6n = 15
4m − 6n = −20
−      +        +       
5m         = 35

∴ m = `35/5`

∴ m = 7

Substituting m = 7 in equation (1),

3m − 2n = 5

∴ 3(7) − 2n = 5

∴ 21 − 2n = 5

∴ − 2n = 5 − 21

∴ − 2n = −16

∴ n = `(-16)/-2`

∴  n = 8

Substituting the values of m and n,

The length of the rectangle = 5m + n

= 5 × 7 + 8

= 35 + 8

= 43

The breadth of the rectangle = m + n − 3

= 7 + 8 − 3

= 15 − 3

= 12

∴ The length of the rectangle is 43 cm and its breadth is 12 cm.