Evaluating Area When Side Is a Variable

Q.

If each side of a square is doubled, then find the increase percentage of its area.

1. 300 %

2. 400 %

3. 350 %

4. 200 %

Q.

If $x+x^{-1}=11$, evaluate $x^2+x^{-2}$.

1. 119

2. 120

3. 122

4. 121

Q.

Substituting $x=-3$ in $x^2+5x$ gives $3^2+5(-3)=-9-15=-24.$

1. True

2. False

Q. A rectangular park has length and breadth of 2 km and 1 km respectively. Due to the metro construction, the authority reduces the length and breadth of the park by $x$ km. Find the new area of the park in terms of $x$.

1. $-x^2+3x+2$
2. $x^2-3x-2$
3. $x^2+3x+2$
4. $x^2-3x+2$

Q.

The length and breadth of a rectangle are extended by x units each. The sides of the original figure were 1 unit and 2units respectively. The figure given below represents the data given above.

1. True

2. False

Q.

The length and breadth of a rectangle are extended by 2 units each. The sides of the original figure were 1 unit and 7units respectively.

From the above, we can conclude that area of the new figure will be 27

1. True

2. False

Q. The product of$8x+3y$ and $3x^2$ is .

1. $24x^3+9x^{2}y$
2. $8x^3+9x^{2}y$
3. $24x^2+9x^{2}y$
4. $24x^3+9x^{3}y$

Q.

The difference of area of two squares is A. The difference of their perimeters is p. Then the sum of their perimeters is ______ .

1. 4A/p

2. 16A/p

3. 8A/p

4. 2A/p

Q.

A rectangle's sides are extended by 3 m. The new area of the figure is given by the expression: a(x) = $x^2+7x+4$. $x$ is the extension of sides. What is the new area ?

1. 14 square meters

2. 24 square meters

3. 34 square meters

4. 54 square meters

Q. Length and width of rectangle are $(x+4)$ & $(x-1)$, then the area of the rectangle is.

1. $x^2+3x-4$
2. $x^2+3x+4$
3. $x^2-3x-4$

Q.

A rectangle's sides are extended by 5 m. The new area of the figure is given by the expression: $a\left(x\right)=x^3+7x+8$. $x$ is the extension of sides. What is the new area?

1. 168 square meters

2. 158 square meters

3. 178 square meters

4. 198 square meters

Q. A rectangle's sides are extended by 3 m. The new area of the figure is given by the expression: a(x) = $x^2+7x+4$. $x$ is the extension of sides. What is the new area?

Q.

Simplify: (x + 3)(x + 3).

1. 

2. 

3. 

4. 

Q.

The extension of sides of the original rectangle is 2. The sides of the original figure are 1 and 7. Area of new figure is 27

1. True

2. False

Q.

A rectangle's sides are extended by 5 m. The new area of the figure is given by the expression: $a\left(x\right)=x^3+7x+8$. $x$ is the extension of sides. What is the new area?

1. 168 square meters

2. 158 square meters

3. 178 square meters

4. 198 square meters

Q.

$\text{Given the area of rectangle is}A=25a^2-35a+12.\text{The length is given}\text{as}(5a-3).\text{Find the width of the}\text{rectangle.}$

1. $4a-5$

2. $5a-3$

3. $5a-4$

4. $a-4$

Q. What is the geometrical expansion of the identity: $(12x+5)(12x+3)$?

Q. Inequation Solve: 1/x-12

Q.

If the adjacent sides of a rectangle are 2a and 5b, then its area is

1. 2a+5b

2. 2ab

3. 10ab

4. 5ab

Q. Verify and expand the identity: $(x+1)(x+4)$ geometrically.

Q.

If the length and breadth of a rectangle are $(x^2-x+2)$ cm and $(x^2+x-2)$ cm respectively, find the area of the rectangle.

1. $(x^4-5x^3-x^2$) sq cm

2. $(x^4-x^3-4x^2+4$) sq cm

3. $(x^4-x^3-x^2-4x$) sq cm

4. $(x^4-x^2+4x-4$) sq cm

Q.

A rectangle's sides are extended by 3 m. The new area of the figure is given by the expression: a(x) = $x^2+7x+4$. $x$ is the extension of sides. What is the new area ?

1. 14 square meters

2. 24 square meters

3. 34 square meters

4. 54 square meters

Q. If each side of a square, of side a, is doubled, find the new area.

1. $a^2$
2. $a^4$
3. 4$a^2$
4. 4$a^4$

Q.

Consider six squares with sides of different lengths.The length of side of square is in direct proportion to:

1. Perimeter of the square

2. Area of the square

3. Both of these

4. None of these

Q. Length and width of rectangle are $(x+4)$ & $(x-1)$, then the area of the rectangle is.

1. $x^2+3x-4$
2. $x^2+3x+4$
3. $x^2-3x-4$

Q. Find the number of shot in an incomplete square pile of $16$ courses, having $12$ shot in each side of the top.

Q.

Find the area of a rectangle whose length is $5xy$ units and breadth is $8x{y}^2$ units.

1. $40x^2$$y^2$ square units

2. $40x{y}^3$ square units

3. $40xy$ square units

4. $40x^2$$y^3$ square units

Q.

The length of a rectangle is $4a$ metres and its area is $72a^2$ sq m, the breadth of the rectangle is :

1. 12a

2. 18a

3. 24a

4. 72 a

Q.

The area of a rectangle having length and width as $5xy$ and $9y$ respectively is $45xy$.

1. False

2. True

Q. Length and width of rectangle are $(x+4)$ & $(x-1)$, then the area of the rectangle is.

1. $x^2+3x-4$
2. $x^2+3x+4$
3. $x^2-3x-4$