An artist is deciding between two different triangular shapes to use for a sculpture. The first triangle has a base of 20 feet and a height of 5 feet. The second triangle has a base of 25 feet. If the two triangles have the same area, what is the height of the second triangle.
the bot is WRONG AGAIN!!!
area of 1st = (1/2)(20)(5) = 50
area of 2nd = (1/2)(25)(h) = 25h/2
25h/2 = 50
25h = 100
h = 4
To find the height of the second triangle, we can set up an equation using the formula for the area of a triangle.
The formula for the area of a triangle is:
Area = (1/2) * base * height
Let's denote the height of the second triangle as 'h'. Given that the base of the second triangle is 25 feet and the area of both triangles is the same, we can set up the equation as follows:
(1/2) * 20 * 5 = (1/2) * 25 * h
Simplifying the equation:
100 = 12.5h
To solve for h, divide both sides of the equation by 12.5:
100 / 12.5 = h
Hence, the height of the second triangle is 8 feet.
To find the height of the second triangle, we need to compare the areas of the two triangles and set them equal to each other.
The area of a triangle is given by the formula: A = (1/2) * base * height.
We'll start by finding the area of the first triangle:
Area of first triangle = (1/2) * 20 feet * 5 feet = 50 square feet.
We know that the two triangles have the same area, so we can set up an equation like this:
50 square feet = (1/2) * 25 feet * h2
Where h2 represents the height of the second triangle.
Simplifying the equation:
50 square feet = (25/2) * h2
To solve for h2, we'll isolate it:
h2 = (50 square feet) / (25/2)
To divide by a fraction, we can multiply by its reciprocal:
h2 = (50 square feet) * (2/25)
Now we can calculate the height of the second triangle:
h2 = (50 square feet) * (2/25) = 100/25 = 4 feet.
Therefore, the height of the second triangle is 4 feet.