Question

An a framed cabin is shaped like an iscoles triangle with legs of 24 feet the floor of the cabin is a rectangle that is twice as long than it is wide with an area of 1152. A loft is added by installing a floor that attaches 5/8 up the legs. Find the area of the loft

Answer 1

The area of the loft is the area of a triangle with base 24 feet and height 9 feet, which is 108 square feet.

Step-by-step explanation:

To find the area of the loft, we first need to determine the dimensions of the loft. The floor of the cabin is a rectangle that is twice as long than it is wide, with an area of 1152. Let's let the width of the floor be x. Since the length is twice the width, the length of the floor is 2x.

So, the area of the floor is x * 2x = 2x^2 = 1152. We can solve this equation by dividing both sides by 2, giving us x^2 = 576. Taking the square root of both sides, we find that x = 24.

Now that we know the width of the floor is 24 feet, we can calculate the dimensions of the loft. The loft attaches 5/8 up the legs of the triangle, which is 5/8 * 24 = 15 feet. The height of the loft is therefore 24 - 15 = 9 feet. The area of the loft is the area of a triangle with base 24 feet and height 9 feet, which is (1/2) * 24 * 9 = 108 square feet.