Question

Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden..​

Answer 1

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Solution:

Given, half the perimeter of a rectangular garden = 36 m

so, 2(l+b)/2=36

(l+b)=36 ……….(1)

Given, the length is 4 m more than its width.

Let width = x

And length be x+4

Substituting this in eq(1), we get;

x+x+4=36

2x+4=36

2x=32

x=16

Therefore, width is 16m and length is 16+4 = 20 m.

Q.3: On comparing the ratios a1a2, b1b2, and c1c2, find out whether the following pair of linear equations are consistent, or inconsistent.

(i) 3x + 2y = 5 ; 2x – 3y = 7

(ii) 2x – 3y = 8 ; 4x – 6y = 9

Solutions:

(i) Given : 3x + 2y = 5 or 3x + 2y -5 = 0

and 2x – 3y = 7 or 2x – 3y -7 = 0

Comparing the above equations with a1x + b1y + c1=0

And a2x + b2y + c2 = 0

We get,

a1=3, b1= 2, c1= -5

a2=2, b2=-3, c2=-7

a1/a2 = 3/2, b1/b2 = 2/-3, c1/c2 = -5/-7 = 57

Since, a1/a2≠b1/b2

Hence, the lines intersect each other at a point and have only one possible solution. The equations are consistent.

(ii) Given 2x – 3y = 8 and 4x – 6y = 9

Therefore,

a1=2, b1= -3, c1= -8

a2=4, b2=-6, c2=-9

a1/a2=2/4=1/2, b1/b2=3/6=1/2, c1/c2=8/9

Since, a1/a2=b1/b2≠c1/c2

Therefore, the lines are parallel to each other and they have no possible solution. Hence, the equations are inconsistent.

Answer 2

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