SOLUTION: in an isosceles triangle each of the equal sides is 10 . If the area of the triangle is less than 48 sq m which of the following is a possible measure of the third side

Algebra ->  Triangles -> SOLUTION: in an isosceles triangle each of the equal sides is 10 . If the area of the triangle is less than 48 sq m which of the following is a possible measure of the third side      Log On


   

Question 866876: in an isosceles triangle each of the equal sides is 10 . If the area of the triangle is less than 48 sq m which of the following is a possible measure of the third side
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Base of b, for the isosceles triangle, two equal sides 10; and altitude h. The altitude forms two right triangles each of base b/2 and hypotenuse 10. Difficult to draw on this site system, so draw this on paper yourself to see.

This is not the complete solution, but most of the way to get to it.

Pythagorean theorem lets you use b/2 and the hypotenuse 10, to get h, the altitude.
h%5E2%2B%28b%2F2%29%5E2=10%5E2
h%5E2=100-%28b%2F2%29%5E2
h=sqrt%28100-b%5E2%2F4%29
h=...
h=%281%2F2%29sqrt%28400-b%5E2%29
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Using A=%281%2F2%29b%2Ah in general, b is the base of the isosceles triangle
want %281%2F2%29b%2A%281%2F2%29sqrt%28400-b%5E2%29%3C48 as specified.
%281%2F4%29b%2Asqrt%28400-b%5E2%29%3C48
highlight_green%28b%2Asqrt%28400-b%5E2%29%3C192%29, important rule about the base of this isosceles triangle.

This limit on b will be somewhere around 12, based on using a graphing tool.