CBSE Class 10-Mathematics: Chapter –3 Pair of Linear Equation in Two Variables Part 7

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2 Mark Questions

Question 1:

Half the perimeter of a rectangle garden, whose length is more than its width, is . Find the dimensions of the garden.

Answer:

Let length of rectangular garden metres

Let width of rectangular garden metres

According to given conditions, perimeter

And

Adding eq. (i) and (ii),

Subtracting eq. (ii) from eq. (i),

Hence, length = 20 m and width = 16 m

Question 2:

Draw the graphs of the equations and . Determine the coordinates of the vertices of the triangle formed by these lines and theaxis and shade the triangular region.

Answer:

For equation , we have following points which lie on the line

points which lie on the line

For equation , we have following points which lie on the line

points which lie on the line

graphs that points of intersection of the lines

Graphs That Points of Intersection of the Lines

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We can see from the graphs that points of intersection of the lines with the x–axis are and .

Question 3:

The age of two friends Ani and Biju differ by years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by years. Find the ages of Ani and Biju.

Answer:

Let the age of Ani and Biju be years and years, respectively.

Age of Dharam years and Age of Cathy years

According to question,

And

Subtracting (1) from (2), we obtain

Age of Ani years

Age of Biju yearsAgain, According to question,

And

Adding (3) and (4), we obtain:

Age of yearsAge of Biju years