Question

translate the following verbal sentences to mathematical sentence. Then express into quadratic equations in terms of x.

1. the length of the floor is 8 m longer than it's width and it's area is 0.36m²

2.the length of the floor is 8 longer than it's width and there is 20 square meters.

3. the length of a plywood is 0.9 m more than its width and it's area is 0.36 m²

4. the area of rectangle whose length is six less than twice is width is thirty-six.

5.the width of a rectangle plot is 5m less it's length and it's area is 84 m²​

Answer 1

Answer:

— Then express into quadratic equations in terms of x. 1. ... 1. the length of the floor is 8 m longer than it's width and it's ... is 0.9 m more than its width and it's area is 0.36 m²

Answer 2

The quadratic equations are shown below:

1. Area of floor:$\bf {x}^{2} + 8x - 0.36= 0$
2. Area of floor:$\bf {x}^{2} + 8x - 20 =0$
3. Area of plywood: $\bf {x}^{2} + 0.9x - 0.36=0$
4. Area of rectangle: $\bf 2{x}^{2} -6x - 36 = 0$
5. Area of rectangle: $\bf {x}^{2} -5x - 84 = 0$

1. Given:

• The length of the floor is 8 m longer than it's width and it's area is 0.36m².

To find:

• Translate the following verbal sentences to mathematical sentence. Then express into quadratic equations in terms of x.

Solution:

Let the width of the floor be 'x' metres.

Then length of floor is $(x + 8) \: m$

Area of rectangle= $\bf length \times breadth$

Area of floor: $x(x + 8) = 0.36$

Area of floor: $\bf {x}^{2} + 8x - 0.36 = 0$

2. Given:

• The length of the floor is 8 longer than it's width and the area is 20 square meters.

To find:

• Translate the following verbal sentences to mathematical sentence. Then express into quadratic equations in terms of x.

Solution:

Let the width of the floor be 'x' metres.

Then length of floor is $(x + 8)m$

Area of floor: $x(x + 8) = 20$

Area of floor :$\bf {x}^{2} + 8x - 20 = 0$

3. Given:

• The length of a plywood is 0.9 m more than its width and it's area is 0.36 m²

To find:

• Translate the following verbal sentences to mathematical sentence. Then express into quadratic equations in terms of x.

Solution:

Let the width of the plywood be 'x' metres.

Then length of floor is $(x + 0.9) \: m$

Area of rectangle= $length \times breadth$

Area of plywood :$x(x + 0.9) = 0.36$

Area of plywood :$\bf {x}^{2} + 0.9x - 0.36 = 0$

4.Given:

• The area of rectangle whose length is six less than twice its width, is thirty-six.

To find:

• Translate the following verbal sentences to mathematical sentence. Then express into quadratic equations in terms of x.

Solution:

Let the width of the rectangle be 'x' metres.

Then length of rectangle is $(2x -6)m$

Area of rectangle: $x(2x -6) = 36$

Area of rectangle: $\bf 2{x}^{2} -6x - 36 = 0$

5.Given:

• The width of a rectangle plot is 5m less it's length and it's area is 84 m²

To find:

• Translate the following verbal sentences to mathematical sentence. Then express into quadratic equations in terms of x.

Solution:

Let the length of the rectangle be 'x' metres.

Then width of rectangle is $(x -5)m$

Area of rectangle: $x(x -5) = 84$

Area of rectangle: $\bf {x}^{2} -5x - 84 = 0$

Thus,

The quadratic equations are shown below

1. Area of floor:$\bf {x}^{2} + 8x - 0.36= 0$
2. Area of floor:$\bf {x}^{2} + 8x - 20 =0$
3. Area of plywood: $\bf {x}^{2} + 0.9x - 0.36=0$
4. Area of rectangle: $\bf 2{x}^{2} -6x - 36 = 0$
5. Area of rectangle: $\bf {x}^{2} -5x - 84 = 0$

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