West Bengal Board Solutions for Chapter: Dividing a Line Segment Into Three or Five Equal Parts, Exercise 2: Let's work out - 23

Rihana drew a straight line segment $PQ$ of length $10 \mathrm{cm}$. I divided line segment $PQ$ in five equal parts by scale and compass. Let's verify by scale each part of the segment is $2 \mathrm{cm}$ or not. 

Ajij divided a line segment $XY$ of length $12 \mathrm{cm}$ in some parts in such a way that each part is of length $2.4 \mathrm{cm}$. First decide how many parts are there and then divide the line $XY$ into that number of equal parts. 

Anoara drew a triangle $ABC$ in her exercise book. We bisect side $BC$ by compass and then draw the median $AD$. I trisect $AD$ in $AE, EF \text{and} FD$. Now we join $B$ and $F$ by scale and extended it to $X$ such that it intersect $AC$ at $X$. Measuring by scale we see, $AX=$_____ $CX$ (Let's put the number) 

Let's divide a line segment of length $12.6 \mathrm{cm}$ into $7$ equal parts, by scale and compass. Using the above construction let's draw an equilateral triangle of length $7.2 \mathrm{cm}$. 

Ramu Pradhan drew a parallelogram $ABCD$ where $AB=6 \mathrm{cm}, BC=9 \mathrm{cm} \text{and} \angle ABC=60°$. Let's select two points $P \text{and} Q$ on diagonal $BD$ such that $BP=PQ=QD$. Let's write the nature of the quadrilateral $APCQ$ joining the points $A, P; P, C; C, Q \text{and} Q, A$. 

Sujata drew $3$ line segments of length $4 \mathrm{cm}, 6 \mathrm{cm} \text{and} 10 \mathrm{cm}$. By scale and compass Rahul bisects the $1\mathrm{st}$ line segment, trisect the $2\mathrm{nd}$ line segment and divide $3\mathrm{rd}$ line segment into five equal parts. Sabnam drew a triangle $PQR$ taking $\frac{1}{2}$ of first line segment, $\frac{1}{3}$ of the $2\mathrm{nd}$ line segment and $\frac{1}{5}\mathrm{th}$ of the $3\mathrm{rd}$ line segment. Let's classify the triangles on the basis of their sides.