Math, asked by Anonymous, 11 hours ago

the perimeter of a rectangle is hundred metre if the length is decreased by 2 and the breadth is increased by 3 the area increased by 44 metre square find the length of breadth of rectangle

Answers

Answered by Anonymous

Answer:

let the length of the given rectangle be x m.

therefore perimeter of the given rectangle is 100m

=> perimeter = 2(length + breadth)

=> 100 = 2(x + breadth)

=> x + breadth

breadth = (50-x)m

area of the given rectangle is length × breadth

= x (50-x)m²

new length = (x - 2)m

new breadth = ( 50 - x + 3)

= (53-3)x

therefore the area of the new rectangle = ( X - 2) (53 - x) m²

according to the given condition

area of new rectangle - area of given rectangle is 44

i.e. (x-2) (53-x) - x (50-x) = 44

or 53x - x² - 106 + 2x - 50x + x² = 44

or 5x - 106 = 44

i.e. 5x = 150

or x = 150/5 = 30

the length of the given rectangle is 30 m

and the breadth of the given rectangle is (50 - 30)m

= 20m

$\huge\mathfrak\blue{verification}$

area of the given rectangle = (30×20)m²

= 600m²

new length is( 30 - 2) = 28 m

new breadth is equal to (20+3) m = 23m

area of new rectangle (28 × 23)m² = 644m²

area of new rectangle - area of the given rectangle

=> (644 - 600)m²

=> 44 m² which is the same as given and solution is verified