Question
Construct a quadrilateral PQRS, in which $\angle\text{PQR}=45^\circ,$ $\angle\text{QRS}=90^\circ,$ QR = 5cm, PQ = 9cm and Rs = 7cm.
✓
Answer
Steps of construction:Step I: Draw QR = 5cm.
Step II: Construct $\angle\text{PQR}=45^\circ$ at Q.
Step III: With Q as the centre and radius 9cm, cut off QP = 9cm.
Step IV: Construct $\angle\text{QRS}=90^\circ$ at R.
Step V: With R as the centre and radius 7cm, cut off RS = 7cm. Since, the line segment PQ and RS intersect each other, the quadrilateral cannot be constructed.
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
Construct ∆DEFG such that l(DE) = 4.5 cm, l(EF) = 6.5 cm, l(DG) = 5.5 cm, l(DF) = 7.2 cm, l(EG) = 7.8 cm.
Solve the following equation and verify your answer:
$\frac{6}{2\text{x}-(3-4\text{x})}=\frac{2}{3}$
→$\frac{6}{2\text{x}-(3-4\text{x})}=\frac{2}{3}$
In the figure, the bisectors of $\angle\text{A}$ and $\angle\text{B}$ meet at a point P. If $\angle\text{C}=100^\circ$ and $\angle\text{D}=50^\circ$, find the measure of $\angle\text{APB}$.
→Construct a quadrilateral ABCD given BC = 6.6cm, CD = 4.4cm, AD = 5.6cm and $\angle\text{C}=100^\circ$ and $\angle\text{C}=95^\circ.$
→Construct a quadrilateral ABCD in which AB = 3.8cm, BC = 3.4cm, CD = 4.5cm, AD = 5cm and $\angle\text{B}=80^\circ.$
→Find the length of the longest rod that can be placed in a room 12m long, 9m broad and 8m high.
Find the area of the pentagon shown in fig. if AD = 10cm, AG = 8cm, AH = 6cm, AF = 5cm, BF = 5cm, CG = 7cm and EH = 3cm.
The denominator of a fraction is greater than its numerator by 12 . If the numerator is decreased by 2 and the denominator is increased by 7 , the new fraction is equivalent to $\frac{1}{2}$. Find the fraction.
→Given below is the frequency distribution of the heights of 50 students of a class:
Draw a histogram representing the above data.
|
Class interval
|
140-145
|
145-150
|
150-155
|
155-160
|
160-165
|
|
Frequency
|
8
|
12
|
18
|
10
|
5
|
Subtract 3x - 4y - 7z from the sum of x - 3y + 2z and -4x + 9y - 11z.