Question

When 3 sides and 2 diagonals are given.
Construct a quadrilateral PQRS in which QR =5 cm, RS = 5.5 cm, PR = 7 cm, PS = 4.5 cm and QS = 5 cm​

Answer 1

Answer:

use this photo and change the measurements please check.

Answer 2

$\huge \underline {\sf {Solution : - }}$

Firstly we may draw a rough diagram for better understanding.

To construct a quadrilateral having 3 sides and 2 diagonal given:-

Step 1 : Draw a line segment SR = 5.5cm

Step 2: Using compass, take the measurement of PS = 4.5cm and placethe compass at S and cut an arc

Step 3: Take another measurement of PR = 7cm and place the compass at R then ,cut an arc . Make the measurement as P

Step 4: Join PS and PR. This will form a triangle.

Step 5 : Again, take the measurement QR = 5cm. Place the compass at R and cut an arc.

Step 6 : Take the measurement of QS = 5cm . Place the compass at S and cut an arc. Make that one as Q

Step 7: Join QR and QS. It forms another triangle. ( Lastly join P and Q for complete quadrilateral).

Now finally, a quadrilateral is constructed.

------------------------

Note:-

• We need 5 elements to construct a quadrilateral.

We can construct a quadrilateral if given :-

1. 4 sides and 1 diagonal
2. 3 sides and 2 diagonal
3. 2 adjacent sides and 3 angles
4. 3 sides and 2 included angels.

---------------