Advertisements
Advertisements
Question
Each side of a rectangle is doubled. Find the ratio between :
(i) perimeters of the original rectangle and the resulting rectangle.
(ii) areas of the original rectangle and the resulting rectangle.
Advertisements
Solution
Let length of the rectangle = x
and breadth of the rectangle = y
(i)
Perimeter P = 2(x + y)
Again, new length = 2x
New breadth = 2y
∴ New perimeter P' = 2(2x + 2y)
= 4(x + y) = 2.2(x + y) = 2P
= `"P"/("P"') = 1/2` i.e. P : P' = 1 : 2
(ii)
Area A = xy
New Area A' = (2x)(2y) = 4xy = 4A
∴ `"A"/("A"') = 1/4` i.e. A : A' = 1 : 4
APPEARS IN
RELATED QUESTIONS
Find the perimeter of a rectangle whose:
length = 10 m and breadth = 8 m
Find the perimeter of an equilateral triangle of side 9.8 cm.
Find the perimeter of a regular hexagon of side 6.5 cm.
If A denotes area of a rectangle, l represents its length and b represents its breadth, find:
l, if A = 48 cm² and b = 6 cm
The perimeter of a rectangular field is 500 m and its length = 150 m. Find:
(i) its breadth,
(ii) its area.
(iii) cost of ploughing the field at the rate of ₹1.20 per square meter.
The length of a rectangle is three times its breadth. If the area of the rectangle is 1875 sq. cm, find its perimeter.
Find the cost of fencing a rectangular park of length 250 m and breadth 175 m at the rate of Rs. 12 per metre.
Four rounds of wire fence have to be put around a field. If the field is 60 m long and 40 m wide, how much wire will be needed?
Find the perimeter of the following figure
Rectangle MNOP is made up of four congruent rectangles (see figure). If the area of one of the rectangles is 8 m2 and breadth is 2 m, then find the perimeter of MNOP.
