A sqaure and a triangle have equal areas.if a side of the square is 10 inches and the base of the triangle is 10,what is the height of triangle draw a diagram to solve the problem
Area of square = 100 square inches
Area of triangle = 1/2 base * height
100 = 1/2(10h)
100 = 5h
20 = h
To find the height of the triangle, we need to first find the area of the square and the area of the triangle.
The area of a square is given by the formula: Area = side^2. Since the side of the square is 10 inches, the area of the square is 10^2 = 100 square inches.
Now, let's find the area of the triangle. The formula for the area of a triangle is: Area = (base * height) / 2. We are given that the base of the triangle is 10 inches, so we can substitute that value into the formula and solve for the height.
100 = (10 * height) / 2.
Multiplying both sides of the equation by 2, we get:
200 = 10 * height.
Dividing both sides of the equation by 10, we get:
20 = height.
Therefore, the height of the triangle is 20 inches.
Now, let's draw the diagram to visualize the problem:
1. Draw a square with a side length of 10 inches. Label it as "Square".
2. Draw a triangle below the square, with the base connecting to the bottom side of the square. Label it as "Triangle".
3. Write down the given values: side length of the square = 10 inches, base of the triangle = 10 inches.
4. Label the height of the triangle as "h".
5. Use the formulas for the area of the square and the area of the triangle to solve for the height of the triangle:
Area of square = side^2 = 10^2 = 100 square inches.
Area of triangle = (base * height) / 2 = (10 * h) / 2.
Since the areas of the square and the triangle are equal, we can equate them:
100 = (10 * h) / 2.
Solve for h:
200 = 10 * h.
h = 20 inches.
Therefore, the height of the triangle is 20 inches.