Question

Madhu's flower garden is now a square. If she enlarges it by increasing the width 1 metre and the length 3 metres, the area will be 19 sq metres more than the present area. What is the length of a side now? ​

Answer 1

Solution :

Madhu's flower garden is now a square.

If she enlarges it by increasing the width by 1 metre, and the length by 3 metres, the area will be 19 square metres more than the present area.

We have to find the length of the side of her flower garden.

Let us start by denoting that by a variable.

Say, the length of the side of her flower garden is a.

Area of the garden is a²

If the width is increased by 1 m

New Width is (a + 1) m

If the length is increased by 3 m

New length is (a + 3) m

New area is

(a+1)(a+3)

Now, the new area is 19 square metres more than the present area

(a+1)(a+3) = a² + 19

a² + 3a + a + 3 = a² + 19

>> 4a + 3 = 19

>> 4a = 16

>> a = 4

Thus, the length of the side of her square garden is 4m .

Answer : The length of the side is 4m.

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Answer 2

CONCEPT :-

• We first assume the length of a side at present and find its area. Then we enlarge the sides and find the area of the rectangle garden. We take the difference as 19. We solve the algebraic equation to get the solution of the variable.

QUESTION :-

• Madhu's flower garden is now a square. If she enlarges it by increasing the width 1 metre and the length 3 metres, the area will be 19 sq metres more than the present area. What is the length of a side now?

GIVEN :-

• Madhu's flower garden is now a square. If she enlarges it by increasing the width 1 metre and the length 3 metres, the area will be 19 sq metres more

TO FIND :-

• What is the length of a side now = ?

SOLUTION :-

Let the length be x cm

Then, Breadth = x cm

A.T.Q. (x + 1)(x + 3) = x² + 19

x² + x + 3x + 3 = x² + 19

x² + 4x - x² = 19 - 3

4x = 16

x = 4

Length = x = 4 m.

ADDITIONAL INFORMATION :-

• We can see the enlargement of the sides increases the area of the square to the area of the rectangle. The formula for the area in both cases is the multiplication of the consecutive sides. In the case of squares, the sides are equal and that's why the area is the square of the side length.