Triangle as Part of Rectangle

Q.

A wire when bent in the form of an equilateral triangle encloses an area of $64\sqrt{3}c{m}^2.$ The area enclosed by the same wire when bent to form a square is ___ $c{m}^2$

1. 81

2. 100

3. 144

4. 16

Q. In the figure given, PR = 22 cm, SN = MQ = 3 cm. What is the area of PQRS?

1. 66 $c{m}^2$
2. 63 $c{m}^2$
3. 34 $c{m}^2$
4. 198 $c{m}^2$

Q. A wire when bent in the form of an equilateral triangle encloses an area of $64\sqrt{3}c{m}^2.$ Then, find the area enclosed by the same wire when bent to form a square.

Q.

Ted bought a new TV set. He decided to keep it on a shelf in the corner of the room at some height so that the view gets better. If AB = AC = 48 inches, is the space enough for a TV with an area of the base (as isosceles right triangle shape) equal to 1200 square inches so that no part of the TV lies outside the shelf? If not, what should be the minimum length of AB?

​

1. No, 49.5

2. Yes

3. No, 48.5

4. No, 49

Q. In the figure given, PR = 22 cm, SN = MQ = 3 cm. What is the area of PQRS?

1. 66 $c{m}^2$
2. 63 $c{m}^2$
3. 34 $c{m}^2$
4. 198 $c{m}^2$

Q.

Ted bought a new TV set. He decided to keep it on a shelf in the corner of the room at some height so that the view gets better. If AB = AC = 48 inches, is the space enough for a TV with an area of the base (as isosceles right triangle shape) equal to 1200 square inches so that no part of the TV lies outside the shelf? If not, what should be the minimum length of AB?

​

1. No, 49.5

2. Yes

3. No, 48.5

4. No, 49

Q. If the total area of the given figure is 662 sq. in, find the value of unknown length 'y' (in inches).

1. 6
2. 8
3. 9
4. 12

Q. The area of a square is $36c{m}^2$. If the side of the square is equal to the side of an equilateral triangle, then find the area of the triangle.

Q. The perimeters of two similar triangles ABC and PQR are 60 cm and 48 cm respectively If PQ=8 cm length of AB is

1. $10cm$
2. $8cm$
3. $4cm$
4. $6cm$

Q.

A wire when bent in the form of an equilateral triangle encloses an area of $64\sqrt{3}c{m}^2.$ The area enclosed by the same wire when bent to form a square is ___ $c{m}^2$

1. 16

2. 81

3. 100

4. 144

Q. What is the area of the rectangle having vertices A, B, C and D with position vectors $-\hat{i}+\frac{1}{2}\hat{j}+4\hat{k},\hat{i}+\frac{1}{2}\hat{j}+4\hat{k},\hat{i}-\frac{1}{2}\hat{j}+4\hat{k}$ and $-\hat{i}-\frac{1}{2}\hat{j}+4\hat{k}$ ?

1. 1/2 square unit
2. 1 square unit
3. 2 square unit
4. 4 square unit

Q. In a $\Delta ABC$ if AB + BC = 12 cm, BC + CA = 14 cm CA + AB = 18 cm then the perimeter of the triangle is__

1. 22 cm
2. 44 cm
3. None of these
4. 20 cm