Answer:
24 inches.
Explanation:
In order for a triangle to be obtuse, one of its angles must be greater than 90 degrees. In a right triangle, the angle opposite the hypotenuse is always 90 degrees, so in order for the triangle to be obtuse, the hypotenuse must be the longest side.
To find the lowest whole number side length in inches that would ensure that the triangle is obtuse, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
a^2 + b^2 < c^2
If we take the base 48cm and convert it to inches, 48cm = 48*0.393701 = 18.897638 inches
So the base is 18.897638 inches.
Now we have to find the lowest whole number side length of c so that:
18.897638^2 + b^2 < c^2
358.565744 + b^2 < c^2
We can see that the lowest whole number of c is 24 inches.
So, the lowest whole number side length in inches that would ensure that the triangle is obtuse is 24 inches.