:The length of a rectangle is twice its breadth. If its length is decreased by 55 cm and breadth
is increased by 55 cm, the area of the rectangle is increased by 75 sq.cm. What is the length
of the rectangle?
Answers
Given :-
Length = 2( Breadth)
If Length = L - 55 cm
Then Breadth = B +55 cm
And Area (A') = A + 75 cm²
Solution :-
Area of rectangle = Length × Breadth .
→ Initial Area :-
→ Area (A) = L × B
→ Area (A) = 2B × B .
- → Area (A) = 2B²
→ New Area .
→ Area (A') =( L-55 ) × (B +55)
→ Area (A') = (2B -55) × (B + 55)
→ Area (A') = 2B² + 110 B - 55B - 3025
→ Area (A') = 2B² + 55B - 3025
→ A' = A + 75 [ where A = 2B²]
→ 2B² + 75 = 2B² + 55B - 3025
→ 2B² - 2B² +75 + 3025 = 55B
→ 3100 = 55B
→ B = 3100/55
→ Breadth = 56.36 cm
→ length = 2(56.36)
- → Length = 112.72 cm
Hence the length of the given rectangle is 112.72 cm .
Answer:
Let breadth
=xcm
Then, length=2xcm
Area =x×2x=2x²
New length
=(2x−5)cm
New breadth
=(x+5)cm
New area =(2x-5)(x+5)
Given that, new area = initial area =75sq.
sq.cm. = (2x - 5) (x + 5)
= 2x2 + 75
= ► 2x2 + 10x - 5x - 25 2c2 + 75 → 5x = 100
=> X = 20
Length = 2x = 2 x 20 = 40 cm