Question
Construct a rhombus the lengths of whose diagonals are 6cm and 8cm.
✓
Answer
We know that the diagonals of a rhombus bisect each other.
Steps of construction: Step 1: Draw AC = 6cm. Step 2: Draw a perpendicular bisector (XY) of AC, which bisects AC at O. Step 3: $\text{OB}=\frac{1}{2}(8)\text{cm}$ $\text{OB}=4\text{cm}$ and $\text{OD}=\frac{1}{2}(8)\text{cm}$ Draw an arc of length 4cm on OX and name that point as B. Draw an arc of length 4cm on OY and name that point as D. Step 4: Join AB, BC, CD and AD. Thus, ABCD is the required rhombus, as shown in the figure.
Steps of construction: Step 1: Draw AC = 6cm. Step 2: Draw a perpendicular bisector (XY) of AC, which bisects AC at O. Step 3: $\text{OB}=\frac{1}{2}(8)\text{cm}$ $\text{OB}=4\text{cm}$ and $\text{OD}=\frac{1}{2}(8)\text{cm}$ Draw an arc of length 4cm on OX and name that point as B. Draw an arc of length 4cm on OY and name that point as D. Step 4: Join AB, BC, CD and AD. Thus, ABCD is the required rhombus, as shown in the figure.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
ABC is a right-angled triangle and O is the mid-point of the side opposite to the right angle. Explain why O is equidistant from A, B and C.
Solve the following equation and also check your result in case:
$\frac{(45-2\text{x)}}{15}-\frac{(4\text{x}+10)}{5}=\frac{(15-14\text{x})}{9}$
→$\frac{(45-2\text{x)}}{15}-\frac{(4\text{x}+10)}{5}=\frac{(15-14\text{x})}{9}$
Making use of the cube root table, find the cube root 8.65
A grocer purchased 200kg of rice at Rs 25/kg. He sold 80kg of it at a gain of 10% and 40kg at a loss of 4%. At what rate/kg should he sell the remainder to gain 8% on his total investment?
Two cubes, each of volume $512 cm^3$ are joined end to end, find the surface area of the resulting cuboid.
→If $2 x+3 y=14$ and $2 x-3 y=2$, find the value of $x y$.
[Hint: Use $(2 x+3 y)^2-(2 x-3 y)^2=24 x y$ ]
→[Hint: Use $(2 x+3 y)^2-(2 x-3 y)^2=24 x y$ ]
If the rate of notebooks is Rs 240 per dozen, what is the cost of 3 notebooks ? Also find the cost of notebooks, 24 notebooks and 50 notebooks and complete the following table.
| Number of notebooks (x) | 12 | 3 | 9 | 24 | 50 | 1 |
| Cost (In Rupees) (y) | 240 | __ | __ | __ | __ | 2 |
The following table shows the expenditure incurred by a publisher in publishing a book:
Present the above data in the form of a pie-chart.
|
Items
|
Paper
|
Printing
|
Binding
|
Advertising
|
Miscellaneous
|
|
Expenditure (in %)
|
35%
|
20%
|
10%
|
5%
|
30%
|
A cistern has two inlets A and B which can fill it in 12 hours and 15 hours respectively. An outlet can empty the full cistern in 10 hours. If all the three pipes are opened together in the empty cistern, how much time will they take to fill the cistern completely?
By selling 90 ball pens for for Rs. 160, a person losses 20%. How many ball pens should be sold for Rs. 96 so as to have a profit of 20%.