Question

3.Draw a rectangle PQRS with sides PQ = 6cm and QR = 4 cm. (Need not write Steps of construction) 
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Answer 1

Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.

Answer 2

Answer:

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Step-by-step explanation:

Steps of construction:

Step 1: Draw PQ=5.4 cm.

Step 2: With P as the centre and radius equal to 4 cm, draw an arc.

Step 3: With Q as the centre and radius equal to 4.6 cm, draw another arc, cutting the previous arc at R.

Step 4: Join QR.

Step 5: With P as the centre and radius equal to 3.5 cm, draw an arc.

Step 6: With R as the centre and radius equal to 4.3 cm, draw another arc, cutting the previous arc at S.

Step 7: Join PS and RS.

Thus, PQRS is the required quadrilateral.