*The length and breadth of an aluminum frame are greater than that of a wooden frame by 3 units. The length of the rectangular wooden frame exceeds its breadth by 3 units. If three times the breadth of the wooden frame is added to its perimeter, then it becomes equal to the perimeter of aluminium frame. Which of the following shows the measurements of the wooden frame?*
1️⃣ 2 units and 5 units
2️⃣ 7 units and 4 units
3️⃣ 11 units and 8 units
4️⃣ 9 units and 12 units
Answers
Answer:
2️⃣ 7 units and 4 units
Step-by-step explanation:
Given :-
The length and breadth of an aluminum frame are greater than that of a wooden frame by 3 units. The length of the rectangular wooden frame exceeds its breadth by 3 units. If three times the breadth of the wooden frame is added to its perimeter, then it becomes equal to the perimeter of aluminium frame.
To find :-
Which of the following shows the measurements of the wooden frame?
1️⃣ 2 units and 5 units
2️⃣ 7 units and 4 units
3️⃣ 11 units and 8 units
4️⃣ 9 units and 12 units
Solution :-
Let the length of a rectangular wooden frame be L units
Let the breadth of the rectangular wooden frame be B units
Given that
The length and breadth of an aluminum frame are greater than that of a wooden frame by 3 units
Length of the aluminium frame
= L+3 units
Breadth of the aluminium frame
= B+3 units
and
Given that
The length of the rectangular wooden frame exceeds its breadth by 3 units
Length of the wooden frame = Breadth +3 units
=> L+3 = B+3+3
=> L+3 = B+6
=>L = B+6-3
=> L = B+3 units ---------(1)
We know that
Perimeter of a rectangle (P)=2(l+b) units
Perimeter of the wooden frame
=> P = 2( L+B) units
=> P = 2(B+3+B) units. (from (1))
=> P = 2(2B+3) units
=> P = (4B+6) units ---------(2)
Perimeter of the aluminium frame
=> P = 2(L+3+B+3) units
=> P = 2(L+B+6) units
=> P =2(B+3+B+6) units
=>P =2 (2B+9)
=> P = (4B+18) units -------(3)
Given that
If three times the breadth of the wooden frame is added to its perimeter, then it becomes equal to the perimeter of aluminium frame.
=> 3× B + Perimeter of the wooden frame = Perimeter of the aluminium frame
=> 3B + 4B+6 = 4B+18
=> 7B+6 = 4B+18
=> 7B-4B = 18-6
=> 3B = 12
=> B = 12/3
=> B = 4 units
On Substituting the value of B in (1) then
=> L = 4+3 units
=> L = 7 units
Therefore, L = 7 units and B = 4 units
Answer:-
The length of the wooden frame = 7 units
The breadth of the wooden frame =
4 units
Check :-
L = 7 units and B = 4 units
=> 7=4+3
Length of the wooden frame is 3 more than its breadth
So ,
Length of the aluminium frame = 7+3 = 10 units
Breadth of the aluminium frame = 4+3 = 7 units
Perimeter of the wooden frame
= 2(10+7) units
= 2(17) units
= 34 units --------(1)
Perimeter of the wooden frame
= 2(7+4)
= 2(11)
= 22 units
3 times the breadth of the wooden frame
= 3×4 = 12 units
Sum of The perimeter of the wooden frame and 3 times its breadth
=> 22+12 = 34 units--------(2)
=> Perimeter of the aluminium frame
(1)&(2) are equal.
If three times the breadth of the wooden frame is added to its perimeter, then it becomes equal to the perimeter of aluminium frame.
Verified the given relations in the given problem.
Used formulae:-
- Perimeter of a rectangle (P)=2(l+b) units
- Where, l = Length of the rectangle
- and b = Breadth of the rectangle