In the figure, the sides of a rectangle are
given. The lengths are in cm. Find the length
and breadth of the rectangle.
4x + 2y
2x+y+2
3x-y+3
2x+3y + 4
Answers
Answer:
4x+2y = 2x+3y+4 (opposite sides of a
rectangle are equal)
Eq. 1
2x+y+2 = 3x-y+3 (opposite sides of a
rectangle are equal)
Eq. 2
Solving 1,
2x = y+4
y = 2x-4
Solving 2,
2y = x+1
Substituting the value of y from Eq. 1 to Eq. 2,
2(2x-4) = x+1
4x-8 = x+1
3x = 9
x = 3
Putting the value of x in Eq. 1,
y = 2(3)-4
y = 6-4
y = 2
x = 3 and y = 2
Step-by-step explanation:
Answer:
The length and breadth of the rectangle are 16 cm & 10 cm respectively.
Step-by-step-explanation:
NOTE: Refer to the attachment for the diagram.
We know that,
Opposite sides of a rectangle are congruent.
∴ AB = CD
→ 2x + y + 2 = 3x - y + 3
→ 2x + y - 3x + y = 3 - 2
→ - x + 2y = 1 - - ( 1 )
Also,
BC = AD
→ 2x + 3y + 4 = 4x + 2y
→ 4 = 4x + 2y - 2x - 3y
→ 4x + 2y - 2x - 3y = 4
→ 2x - y = 4 - - ( 2 )
By multiplying equation ( 2 ) by 2, we get,
→ 2 × ( 2x - y ) = 4 × 2
→ 4x - 2y = 8 - - ( 3 )
Now, by adding equation ( 1 ) & equation ( 3 ), we get,
- x + 2y = 1 - - ( 1 )
+
4x - 2y = 8 - - ( 3 )
___________
→ 3x = 9
→ x = 9 ÷ 3
→ x = 3
By substituting x = 3 in equation ( 1 ), we get,
- x + 2y = 1 - - ( 1 )
→ - ( 3 ) + 2y = 1
→ - 3 + 2y = 1
→ 2y = 1 + 3
→ 2y = 4
→ y = 4 ÷ 2
→ y = 2
Now,
Length of rectangle ( AD ) = 4x + 2y
→ AD = 4 × 3 + 2 × 2
→ AD = 12 + 4
→ AD = 16
∴ Length of rectangle = 16 cm
Now,
Breadth of rectangle ( AB ) = 2x + y + 2
→ AB = 2 × 3 + 2 + 2
→ AB = 6 + 2 + 2
→ AB = 8 + 2
→ AB = 10
∴ Breadth of rectangle = 10 cm.
∴ The length and breadth of the rectangle are 16 cm & 10 cm respectively.