Question

1. The side a square is m meters long. The length of a rectangle is 3 meters longer than the side of the square, and the width of the rectangle is 3 meters shorter than the side of the square. Which has a greater area? By how much?

Answer 1

Answer:

Let the width of rectangle is y cm then length of rectangle is y+8 cm

Then area of total rectangle =y(y+8)=y

2

+8ycm

2

If a square side x cm cut in this rectangle whose side is half of width of rectangle

So x=\frac{1}{2}y \Rightarrow y=2x$$

Then area of total rectangle =y(y+8)=y

2

+8ycm

2

put the value y=2x

Then area of rectangle=2x(2x+8)=4x

2

+16xcm

2

Then renaming area =4x

2

+16x−x

2

=(3x

2

+16x)cm

2

Answer 2

The area of the square is greater than the area of rectangle. It is greater by 9 units.

GIVEN

The side a square is m meters long. The length of a rectangle is 3 meters longer than the side of the square, and the width of the rectangle is 3 meters shorter than the side of the square.

TO FIND

Which has a greater area? By how much?

SOLUTION

We can simply solve the above problem as follows;

Let the side of the square = m meter

Length of the rectangle = m + 3 meter

Breath of the rectangle = m-3 meter

We know that,

Area of the square = Side × Side

Area of the square = m² metre. (Equation 1)

And,

Area of the rectangle = L × B

= (m-3)(m+3)

Applying the formula; (a+b)(a-b) = a² - b²

= m²- 9 meters (Equation 2)

From 1 and 2

We can observe that, The area of the square is greater. It is greater by 9 units.

, The area of the square is greater. It is greater by 9 units. #Spj2