Rectangle (in cm) Left Breadth = 2y + 11 Right = 3x + 17 Top Length = x + 3y Bottom =5x-5y

Question

Find its a) length b) breadth c) diagonal?  

 

 

 

 

 

Answer 1

Rectangle left breadth = right breadth

2y + 11 = 3x + 17

3x - 2y + 17 - 11 = 0

3x - 2y = - 6 ---> (1)

Rectangle top length = bottom length

x + 3y = 5x - 5y

4x - 8y = 0 ---> (2)

• Solve the equations (1) & (2).

3x - 2y = - 6 ---> (1)

Multiply each side of equation by negative 4.

- 12x + 8y = 24 ---> (3)

To eliminate the y variable, add the equations (2) & (3).

- 12x + 8y = 24

 4x - 8y = 0

___________

- 8x = 24

x = - 3

Substitute the x in equation (1).

3(- 3) - 2y = - 6

- 9 - 2y = -6

2y = - 3

y = - 1.5

Solution x = - 3 and y = - 1.5.

• Left breadth = 2y + 11 = 2(- 1.5) + 11 = 8

Right breadth = 3x + 17 = 3( - 3) + 17 = 8

Top length = x + 3y = - 3 - 4.5 = - 7.5

Bottom length = 5x - 5y = - 15 + 7.5 = - 7.5

a) Rectangle length = 7.5 cm

b) Rectangle breadth = 8 cm

c) From the pythagorean theorem rectangle diagonal = √[(length)² + (width)²]

Diagonal = √[(7.5)²+ (8)²  ]

               = √(56.25 + 64) = √(120.25)

Diagonal = 10.96 cm.