In rectangle ABCD, AB = 4x – 2y, BC = x + 2y + 5, CD = 3x + y + 6, AD = 3x – y -1 then find the length, breadth and perimeter of that rectangle.
Answers
Use this method for your answer
Given :- In rectangle ABCD, AB = 4x – 2y, BC = x + 2y + 5, CD = 3x + y + 6, AD = 3x – y -1 .
To Find :- The length, breadth and perimeter of that rectangle. ?
Formula used :-
- Opposite sides of a rectangle are equal in measure . So, AB = CD and BC = DA .
- Perimeter of rectangle = 2(Length + Breadth)
Solution :-
→ AB = CD
→ 4x - 2y = 3x + y + 6
→ 4x - 3x - 2y - y = 6
→ x - 3y = 6 ------- Eqn.(1)
and,
→ BC = DA
→ x + 2y + 5 = 3x - y - 1
→ 3x - x - y - 2y = 5 + 1
→ 2x - 3y = 6 --------- Eqn.(2)
Subtracting Eqn.(1) from Eqn.(2),
→ (2x - 3y) - (x - 3y) = 6 - 6
→ 2x - x - 3y + 3y = 0
→ x = 0 .
putting value of x in Eqn.(1),
→ 0 - 3y = 6
→ (-3y) = 6
→ y = (-2)
therefore,
→ AB = 4x - 2y = 4 × 0 - 2 × (-2) = 0 + 4 = 4 unit .
→ BC = x + 2y + 5 = 0 + 2 × (-2) + 5 = 0 - 4 + 5 = 1 unit .
hence,
→ Perimeter of rectangle = 2(AB + BC) = 2(4 + 1) = 10 units .
Hence, the length, breadth and perimeter of that rectangle are 4 units , 1 unit and 10 units respectively .
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