Absolutely, let's calculate the length of the hypotenuse for the given right triangle.
First of all, let's find the base of the triangle. We know that the area of a right-angled triangle is given by the formula 1/2(base)*(height). Since we know the area and the height, we can easily find the base.
Rearranging the formula, we get base = 2*area/height.
Substituting the given values into the formula: base = 2*24/6 = 8.
So, the base of the triangle is 8 inches.
Now, to find the hypotenuse (the longest side of a right-angled triangle), we use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.
Here, these sides are base and height.
So, the hypotenuse is sqrt(base^2 + height^2).
Substituting the values we have: hypotenuse = sqrt(8^2 + 6^2) = sqrt(64 + 36) = sqrt(100) = 10.
Therefore, the length of the hypotenuse is 10 inches.
That's your answer: The base of the triangle is 8 inches and the hypotenuse is 10 inches.