Question

Represent 35

on number line ​

Answer 1

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• We will draw a line segment AB of 3.5 units.

• Step 2: We will produce 3.5 by 1 unit and name the end point as C. So, we get,

• Step 3: We will find the midpoint of AC and name the mid-point as O.

• Step 4: We will draw a semicircle from O taking OA as the radius, so we get,

• Step 5: We will draw a perpendicular line from point B touching the semicircle at point D.

• Step 6: We will get BD is equal to 3.5−−−√3.5 from the calculation below. Then, to represent it in the number line we will draw an arc with point B as the center and BD as the radius to the line and will mark that point as E. So BE will represent 3.5−−−√3.5 in the number line.

• In triangle OBD, we will apply the Pythagoras theorem, so we get,

• BD2=OD2−OB2BD2=OD2−OB2

Now, we know that OD = OC, also we can write OB as OC – BC, so we can write,

BD2=OC2−(OC−BC)2BD2=OC2−(OC−BC)2

• We know that (a−b)2=a2+b2−2ab(a−b)2=a2+b2−2ab, so we can write,

• BD2=OC2−(OC2+BC2−2(OC)(BC))BD2=OC2−OC2−BC2+2(OC)(BC)BD2=2(OC)(BC)−BC2BD2=OC2−(OC2+BC2−2(OC)(BC))BD2=OC2−OC2−BC2+2(OC)(BC)BD2=2(OC)(BC)−BC2

Now, from the figure, we can see that O is the midpoint of AC, so we get OC as half of AC, that is, OC=4.52=2.25OC=4.52=2.25.

Therefore, on putting the values of OC as 2.25 and BC as 1, we get,

BD2=2×2.25×1−1BD2=4.5−1=3.5BD=3.5−−−√BD2=2×2.25×1−1BD2=4.5−1=3.5BD=3.5

Thus, we get BD=3.5−−−√BD=3.5.