Geometry Problem, Detailed solution required.

[AdkAdi]

 

[Harry_the_cat]

And ... what you done so far?

 

[AdkAdi]

And ... what you done so far?

I have drawn the diagram showing the base of the square coinciding with the base of the triangle, but I am unable to understand the point behind the centre of gravity concept which deterred me from proceeding any further, becuase I cannot understand what to do next.

 

[Harry_the_cat]

Do you know how to find the centre of gravity of a triangle?

 

[AdkAdi]

Do you know how to find the centre of gravity of a triangle?

Yes the centroid is the center of gravity of the triangle

 

[Deleted member 4993]

I have drawn the diagram showing the base of the square coinciding with the base of the triangle, but I am unable to understand the point behind the centre of gravity concept which deterred me from proceeding any further, becuase I cannot understand what to do next.

do a Google search for "center of gravity of a triangle" - tell us what you found .

 

[Harry_the_cat]

Yes, do you know the properties of the centroid?

 

[AdkAdi]

O

Yes, do you know the properties of the centroid

Yes, do you know the properties of the centroid?

I do know them, but how to use them in the given problem!?

 

[Deleted member 4993]

Yes the centroid is the center of gravity of the triangle

where is the center located for an isosc elis triangle? Locate it inside your sketch.

 

[Harry_the_cat]

what ratio does the centroid divide the medians?

 

[Harry_the_cat]

Also look for similar triangles. Don't forget that the square is a unit square.

 

[AdkAdi]

where is the center located for an isosc elis triangle? Locate it inside your sketch.

what ratio does the centroid divide the medians?

2:1

 

[AdkAdi]

Also look for similar triangles. Don't forget that the square is a unit square.

It would be better if you could help me with the solution please!

 

[AdkAdi]

where is the center located for an isosc elis triangle? Locate it inside your sketch.

Can you provide me with a proper solution?

 

[Harry_the_cat]

Not in the long run. It would be better for you if you put thought into it and arrived at the solution yourself. We are here to help, not just give out answers.

 

[Harry_the_cat]

Can you provide me with a proper solution?

No.

 

[AdkAdi]

Not in the long run. It would be better for you if you put thought into it and arrived at the solution yourself. We are here to help, not just give out answers.

Ok, thanks for the hints. I will give it a try once again though I have tried it many times earlier.

 

[Harry_the_cat]

Redraw your diagram, roughly to scale. You now know the height of the isosceles triangle. You need to calculate the base.
Look for similar triangles. You may need to let one of the unknown lengths be x and use the property of ratios of sides of similar triangles to calculate x and then the base and then the area!