A right triangle, which has an area of 24 square feet, consists of one leg that is three times longer than the other leg. To determine the length of the longest side, we need to solve for this value.
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✓ Correct answer: D. 12.6For a right triangle, the area can be calculated using the formula:<br/><br/>Area = (1/2) * base * height<br/><br/>Let's assume that the shorter leg of the triangle is x feet. According to the given information, the longer leg is three times longer than the shorter leg, so the longer leg would be 3x feet.<br/><br/>Using the formula for the area of a triangle, we can set up the equation:<br/><br/>24 = (1/2) * x * 3x<br/><br/>48 = 3x^2<br/><br/>16 = x^2<br/><br/>x = 4<br/><br/>So, the shorter leg of the triangle is 4 feet.<br/><br/>To find the length of the longest side, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the longest side is the hypotenuse.<br/><br/>Let's denote the length of the longest side (hypotenuse) as c.<br/><br/>Using the Pythagorean theorem, we can set up the equation:<br/><br/>c^2 = (4^2) + (3(4))^2<br/><br/>c^2 = 16 + 144<br/><br/>c^2 = 160<br/><br/>c = √160<br/><br/>c ≈ 12.6<br/><br/>So, the length of the longest side (hypotenuse) is approximately 12.6 feet.<br/><br/>Therefore, the correct answer is B) 12.6.
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