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 triangles have the same area, what is the height of the second triangle
We can use the formula for the area of a triangle which is:
Area = (base * height) / 2
Since the first triangle has a base of 20 feet and a height of 5 feet, we can calculate its area:
Area of first triangle = (20 * 5) / 2 = 50 square feet
Since the two triangles have the same area, we can set the equation:
(25 * height) / 2 = 50
Simplifying the equation, we get:
25 * height = 100
Dividing both sides by 25, we get:
height = 4
Therefore, the height of the second triangle is 4 feet.
To find the height of the second triangle, we can use the formula for the area of a triangle, which is given by:
Area = (base * height) / 2
We are given that the first triangle has a base of 20 feet and a height of 5 feet. Let's calculate its area:
Area1 = (20 * 5) / 2
= 100 / 2
= 50 square feet
Since the two triangles have the same area, the area of the second triangle must also be 50 square feet. We are given the base of the second triangle as 25 feet. Let's substitute these values and solve for the height of the second triangle:
50 = (25 * height) / 2
Let's simplify the equation:
50 * 2 = 25 * height
100 = 25 * height
Now, to solve for the height, we can divide both sides of the equation by 25:
100 / 25 = height
4 = height
Therefore, the height of the second triangle is 4 feet.
To find the height of the second triangle, we need to first calculate the area of the first triangle, which we can use as a reference.
The formula to calculate the area of a triangle is:
Area = (base * height) / 2
For the first triangle:
Area = (20 feet * 5 feet) / 2
= 100 square feet
Since we know that the two triangles have the same area, we can set up the following equation:
100 square feet = (25 feet * height) / 2
To isolate the height, we can multiply both sides of the equation by 2 and then divide by 25:
100 square feet * 2 = 25 feet * height
200 square feet = 25 feet * height
Now, we can solve for the height by dividing both sides of the equation by 25:
height = 200 square feet / 25 feet
height = 8 feet
Therefore, the height of the second triangle is 8 feet.