Rectangle

Q.

The diagonals do not necessarily bisect the interior angles at the vertices in a

(a) rectangle (b) square

(c) rhombus (d) all of these

Q. Which of these is not a property of a rectangle?

1. Opposite sides are equal
2. Adjacent sides are perpendicular to each other
3. The diagonals are of equal length and intersect perpendicularly
4. The diagonals are of equal length and bisect each other

Q. All rectangles are parallelograms.

1. True
2. False

Q.

The length and breadth of a rectangle are in the ratio 4 : 3. If the diagonal measures 25 cm, then the perimeter of the rectangle is

(a) 56 cm (b) 60 cm

(c) 70 cm (d) 80 cm

Q.

The sides of a rectangle are in the ratio $5:4$ and its perimeter is $90cm$. Find its length and breadth.

Q.

Question 69

Solve the following:

$\frac{2y-3}{4}-\frac{3y-5}{2}=y+\frac{3}{4}$

Q.

What is the angle formed between the diagonals of a square?

Q.

Find the length of the diagonal of a rectangle whose sides are 12 cm and 5 cm.

Q.

One of the diagonal of a rhombus is equal to one of its side. Find the angles of the rhombus

Q.

Draw a trapezium ABCD in which AB||DC, AB=7 cm, BC=5 cm, AD=6.5 cm and angle B =60°.

Q.

$\square \mathrm{ABCD}$ is a trapezium in which $\mathrm{AB}\left|\right|\mathrm{CD}$ and$\mathrm{AD}=\mathrm{BC}$(see Fig.) .

Show that $\angle \mathrm{A}=\angle \mathrm{B}$ ( [Hint : Extend $\mathrm{AB}$ and draw a line through $\mathrm{C}$parallel to $\mathrm{DA}$ intersecting $\mathrm{AB}$ produced at $\mathrm{E}$.]

Q.

Which of these is not a property of rectangles?

1. Opposite sides are equal.

2. Adjacent sides are perpendicular to each other.

3. The diagonals are of equal length and intersect perpendicularly.

4. The diagonals are of equal length and bisect each other.

Q. The sum of the interior angles of a rectangle is _____.

1. ${360}^{\circ }$
2. ${180}^{\circ }$
3. ${90}^{\circ }$
4. ${135}^{\circ }$

Q. The diagonals of a rectangle bisect each other.

1. True
2. False

Q. If PQRS is a rectangle, then the length of each diagonal is:

1. 144 cm
2. 63 cm
3. 122 cm
4. 120 cm

Q.

How do you solve for $y$ in the equation $2x+y=6$?

Q. ABCD is a rectangle with diagonals AD and BC intersecting at point O. If the length of AO is 6 units, find the length of CB.
[3 MARKS]

Q. A parallelogram with right angles is called a rectangle.

1. False
2. True

Q. Question 112
State whether the statements are True or False.
Diagonals of a rectangle bisect each other at right angles.

Q.

If $a1,a2,a3\dots \dots$are in AP, then the value of $\left[\begin{array}{ccc}{a}_1& a_2& 1\\ a_2& a_3& 1\\ a_3& a_4& 1\end{array}\right]$ is

Q.

In the given figure, ABC is a triangle, right angled at B. If BCDE is a square on the side BC and ACFG is a square on AC, then AD is ____.

1. $AD=BF$

2. $AD>BF$

3. $AD<BF$

4. None of these

Q. Question 156
A playground is in the form of a rectangle ATEF. Two players are standing at the point F and B, where EF = EB. Find the values of x and y.

Q. Question 5
The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram.

Q. In a given rectangle ABCD, diagonals AD and BC intersect at O. If $\angle COD={120}^{\circ }$, what is the value of $\angle OBA$?

1. ${90}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. none of these

Q.

$ABCD$ is a rectangle , if $\angle BPC={124}^{\circ }$ Calculate : $\left(i\right)\angle BAP\left(ii\right)\angle ADP$

Q.

Find the cost of levelling a playground $51m$ long and $40m$wide at $35$ Rs per square meter . Also , find the cost of fencing it at $50$Rs per meter .

Q.

The measures of two adjacent angles of a parallelogram are in the ratio $3:2$. Find the measure of each of the angles of the parallelogram.

Q. The angle between a diagonal and a side of a square is ___.

1. 60 degrees
2. 90 degrees
3. 30 degrees
4. 45 degrees

Q. The sides of a rectangle whose area is 216 $c{m}^2$ are in the ratio 2:3. Find its perimeter.

1. 5 cm
2. 6 cm
3. 30 cm
4. 60 cm

Q. equal is not the property of a rectangle.

1. opposite sides
2. diagonals
3. adjacent sides