Use of Algebraic Expressions in Formula of Area of Figures

Q. Find the perimeter of an isosceles right triangle having an area of $100c{m}^2$.

1. $20(\sqrt{2}+1)$
2. $20(\sqrt{2}-1)$
3. $2(\sqrt{2}+1)$
4. $10(\sqrt{2}+1)$

Q. The area of a rectangular door is 4m + 8n - 12. Which of the following gives its dimensions?

1. 4, m + 2n - 3
2. 4, m + 8n - 12
3. 4, m + 4n - 3
4. 4, 4m + 2n - 4

Q. The base of a triangular field is three times its height. If the cost of cultivating the field is $Rs1080$ per hectare. If the total cost of cultivating the field is $Rs14580$. find its base and height.

Q. A rectangle is 3p cm long and 2p cm wide. Find the perimeter of the rectangle when p = 12.

1. 102 cm
2. 120 cm
3. 210 cm
4. 10p cm

Q. Write in the form of an algebraic expression:​
(ii)Perimeter $\left(P\right)$ of a square is four times its side.​

Q. The area of a rectangular door is 4m + 8n - 12. Which of the following gives its dimensions?

1. 4, m + 2n - 3
2. 4, m + 8n - 12
3. 4, m + 4n - 3
4. 4, 4m + 2n - 4

Q. If the adjacent sides of a rectangle are $(x^2-x+2)$ units and $(x^2+x-2)$ units long, find the area of the rectangle.

1. $(x^4-5x^3-x^2)$ square units
2. $(x^4-x^3-4x^2+4)$ square units
3. $(x^4-x^2+4x-4)$ square units
4. $(x^4-x^3-x^2-4x)$ square units

Q. The length and breadth of a rectangular plot are $l$ and $b$ units respectively. Two rectangular paths each of width $w$ units run inside the plot one parallel to the length and the other parallel to the breadth. What is the total area (in sq. units) of the paths?

1. $(l+w)(b+w)-lb$
2. $lb-(l-w)(b-w)$
3. $(l+b-w)w$
4. $lb-(l-2w)(b-2)$

Q.

The sides of a right angled triangle are 2a cm, (2a+2) cm and (4a -2) cm. What is the length of the shortest side of the triangle if its perimeter is 24 cm?

1. 3 cm

2. 10 cm

3. 6 cm

4. 8 cm