Aa square and a triangle have equal areas. If a side of the square is 10 inches and the base of the triangle is 10 inches, what is the height of the triangle?
let the height be h inches
(1/2)(10)h = 100
solve for h
To find the height of the triangle, we can use the formula for the area of a triangle, which is:
Area = (base * height) / 2
Since the area of the square is equal to the area of the triangle, we can set up the following equation:
Area of square = Area of triangle
Let's calculate the area of the square:
Area of square = (side)^2 = (10 inches)^2 = 100 square inches
Now we have:
100 square inches = (base * height) / 2
We know that the base of the triangle is 10 inches, so we can substitute this value:
100 square inches = (10 inches * height) / 2
To solve for the height, we can rearrange the equation:
(10 inches * height) / 2 = 100 square inches
Multiplying both sides of the equation by 2:
10 inches * height = 200 square inches
Dividing both sides by 10 inches:
height = 200 square inches / 10 inches
Simplifying the right side:
height = 20 inches
Therefore, the height of the triangle is 20 inches.