Question

the length of a rectangle exceeds the breadth by 6.if the length is increased by 3cm and breadth decrease by 2cm,the area remains the same. find the length and breadth of the rectangle

Answer 1

Hi there !!
Answer down here ⬇️⬇️

Given that ,
the length of a rectangle exceeds it's breadth by 6
Let the breadth be x cn
Length = x + 6 cm

Area of triangle = length × breadth
= (x + 6)(x)
= x² + 6x cm²

Given,
if the length is increased by 3cm and breadth decrease by 2cm,the area remains the same

So,
Length = x + 6 + 3 = x + 9 cm
Breadth = x - 2 cm

Area of the new triangle
= (x + 9)(x - 2) cm
= x² + 7x - 18 cm

Also,
the area remain the same , that is , they're equal


Therefore,
the given balanced equation will be formed
x² + 6x = x² + 7x - 18
6x = 7x - 18
x = 18

Thus,the original
Length = x+6 = 18+6 = 24cm
Breadth = x = 18cm

Thus,
the length and breadth are 24cm and 18cm Respectively




Verification :
Area of the original rectangle = 24 × 18 = 432cm²
Under the given conditions,
length will be 27
breadth will be 16
area = 27 × 16 = 432cm³

Hence ,
our answer is correct !

_____________

Hope it helps :D