The length of the base of an isosceles triangle is 5x - 6 The length of a leg is x. The perimeter of the triangle is 153. Find x.

Estimating value of √37.

We know that

and , so

6 < √37 < 7

If we take the average of 6 and 7, we get

Since,

6 < √37 < 6.5

If we take the average of 6 and 6.5 , we get

Since,

6 < √37 < 6.25

If we take the average of 6 and 6.25 , we get

Since,

6 < √37 < 6.125

If we take the average of 6 and 6.125 , we get

Since,

6.0625 < √37 < 6.125

If we take the average of 6.0625 and 6.125 , we get

Since,

6.0625 < √37 < 6.09375

If we take the average of 6.0625 and 6.09375 , we get

Since,

6.078125 < √37 < 6.09375

If we take the average of 6.078125 and 6.09375 , we get

Since,

Therefore,

√37 ≈ 6.0859375.

And if we round it to the nearest tenth, we get

√37 ≈ 6.1

Locating √37 on number line.

In order to locate √37 on number line first draw a line 0 to 6 on number line.

Then draw a perpendicular line segment of 1 unit on number 6 on number line.

Join the number 0 on the number line by the top point of perpendicular line segment on number 6 we drew in above step.

Finally, draw a curve by taking radius as Hypotenuse of the right trinagle form in the diagram shown.

The curve would cut the number line exactly at √37 on number line.