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notsponge [240]
3 years ago
7

POP

Mathematics
1 answer:
icang [17]3 years ago
8 0

Answer:

The dimensions of rectangle are

Length: 15 meters

Breadth: 12 meters

Step-by-step explanation:

Let

x ----> the original length of rectangle

y ---> the original breadth of rectangle

The area of rectangle is

A=xy

1) The area of a rectangle reduces by 20 m2, if its length is increased by I m and the  breadth is reduced by 2 m

A-20=(x+1)(y-2)

A=(x+1)(y-2)+20

A=xy-2x+y-2+20

A=xy-2x+y+18

Remember that

A=xy

substitute

xy=xy-2x+y+18

y=2x-18 -----> equation A

2) The area increases by 12 m², if the length is reduced  by 3 m and the breadth is increased by 4 m.

A+12=(x-3)(y+4)

A=(x-3)(y+4)-12

A=xy+4x-3y-12-12

A=xy+4x-3y-24

Remember that

A=xy

substitute

xy=xy+4x-3y-24

4x-3y=24 -----> equation B

Solve the system of equations A and B by substitution

substitute equation A in equation B

4x-3(2x-18)=24

solve for x

4x-6x+54=24\\2x=30\\x=15\ m

Find the value of y

y=2(15)-18=12\ m

therefore

The dimensions of rectangle are

Length: 15 meters

Breadth: 12 meters

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