the length and breadth of a rectangle are in the ratio 1 ratio 2 if the length in is increased by 2 cm and breadth by 3 cm then the ratio of the perimeter of the new rectangle to the perimeter of the original rectangle is 4.3 find the dimensions of the original Triangle.
Answers
Answer:
length is 50/99,breadth is 100/99
Step-by-step explanation:
given ratio of length(l) and breadth(b) of rectangle is 1/2 i.e,
l/b=1/2
b=2l--------------(1)
perimeter of rectangle is 2(l+b)
if lengtj increased by 2cm,breadth increased by 3cm..
2(l+2+b+3)=2(l+b+5)
perimeter ratio of new rectangle to old is 4.3
2(l+b+5)/2(l+b)=4.3
l+b+5=4.3l+4.3b
3.3l+3.3b=5
l+b=50/33---------(2)
put eq(1) in eq(2)
3l=50/33
l=50/99,hence
b=2l=2(50/33)=100/99
length =10 CM
breadth =5CM
let the ratio of length and breadth of original rectangle = 2x and x
perimeter of rectangle = 2 (l+b)
=2(2x+x)
=2×3x
=6x
when the length is increased by 2cm and breadth by 3cm then
the length=2x+2
the breadth=x+3
the perimeter of the rectangle =2(l+b)
=2{(2x+2) + (x+3)
=2 (3x+5)
=6x+10
the ratio of the new rectangle and the original rectangle = the perimeter of new rectangle /the perimeter of original rectangle
4/3 = 6x+10 / 6x
24x=18x + 30
24x - 18x=30
6x=30
x=30÷6
x=5
length of the original rectangle =2x
=2×5
=10cm
breadth of the original rectangle =x
=x × 5
=5cm