Question

a rectangle field has an area 300sqm and a perimeter of 80m.what are length and width of field
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Answer 1

Answer:

Let the length of the field be L and the width of the field be W

Area of rectangle is given by A=L*B

Perimeter of rectangle is given by P=2(L+B).

Using information given by the question we have the following 2 equations:

L*B = 300 ......(1)

2(L+B) = 80 ......(2)

Since we have two unknowns and two equations, we can solve the simultaneous equation.

From (1):

L=300/B ........(3)

Substitute (3) into (2):

2(300/B+B)=80

Divide by 2 on both sides:

300/B + B = 40

Multiply by B on both sides:

300 + B^2 = 40B

Rearranging,

B^2 -40B + 300 = 0

Factorizing,

(B-30)(B-10) = 0

B = 30 or 10

Checking:

Substitute the values of B into (1), we realise that

If B=30, L=10

If B=10, L=30

Hence the length and breadth are 30cm and 10 cm or vice versa

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