The length of a rectangle is 5cm more than the breadth . If the length is increased by 3cm and breadth by 2cm , the area i s increased by 38cmsquare. Find the original dimensions of th e rectangle
Answers
Answer:
54cm2
Step-by-step explanation:
Let the breadth of the rectangle be Xcm
Then, the length of the rectangle be (x+3)cm
∴ Area of the rectangle =(x+3)×xcm
2
−−−−−(1)
Given that
Length is increased by 9=x+3+9=x+12cm
and, breadth is reduced by 3=x−3cm
Now,
Area of new rectangle (x+12)×(x−3)cm
2
−−−−−(2)
But in the given question we have given that the both area is same
then we can get
(x+3)×x=(x+12)×(x−3)
⇒x
2
+3x=x
2
+12x−3x−36
⇒6x=36
∴x=6
Now,fromequation(1)
Areaoftherectangle=(x+3)×x
=(6+3)6
=54cm
2
.
Answer:
l = b + 5
Area initially = lb = ( b + 5 ) b
A = ( b + 5 ) b ------- 1
Area after modifications = A + 38 cm^2
( l + 3 ) ( b + 2 ) = A + 38
A = ( l + 3 ) ( b + 2 ) - 38 --------2
Comparing both equations
( b + 5 ) b = ( l + 3 ) ( b + 2 ) - 38
b^2 + 5b = ( b + 5 + 3 ) ( b + 2 ) - 38
b^2 + 5b = b^2 + 8b + 2b + 16 - 38
10b - 5b = 22
5b = 22
b = 22/5
= 4.4 cm
l = b + 5 = 4.4 + 5 = 9.4 cm