find the base and height of triangle in ratio 8to 5 and area is 320
let ratio 8x:5x
area of triangle=1/2 bh
320=1/2*8x*5x
320=20x*x
x*x=16
x=4
base=8*4=32
height=5*4=20
The height of a triangle, y, varies directly to the base of the triangle, x, so that when the height is 14 ft the base is 7 ft. If the height of a triangle is 10 ft, what would be the base of the triangle?
To find the base and height of a triangle given the ratio and the area, you can follow these steps:
Step 1: Set up the ratio of the base and height as 8:5.
Let the base be 8x and the height be 5x, where x is a constant.
Step 2: Use the formula to calculate the area of a triangle.
The area of a triangle is given by the formula: A = (base * height) / 2.
Step 3: Substitute the values into the formula.
We are given that the area is 320, so we can write the equation as:
320 = (8x * 5x) / 2.
Step 4: Solve for x.
Multiply both sides of the equation by 2:
640 = 40x^2.
Divide both sides of the equation by 40:
16 = x^2.
Take the square root of both sides to find x:
x = √16 = 4.
Step 5: Find the base and height.
Now that we know the value of x, we can substitute it back into the ratio to find the base and height:
Base = 8x = 8*4 = 32.
Height = 5x = 5*4 = 20.
Therefore, the base of the triangle is 32 units and the height is 20 units.
To find the base and height of a triangle, we need to use the formula for the area of a triangle which is given by the formula A = (1/2) * base * height. We also need to use the given ratio between the base and height.
Let's assume that the base of the triangle is 8x and the height is 5x, where x is a common factor between the base and height.
Since the area of the triangle is given as 320, we can substitute these values into the formula and solve for x:
320 = (1/2) * 8x * 5x
Let's simplify the equation:
320 = 4x^2 * 5
Now, divide both sides of the equation by 4 and 5:
320 / (4 * 5) = x^2
64 = x^2
Next, take the square root of both sides to solve for x:
√64 = √(x^2)
8 = x
Now that we have the value of x, we can find the base and height of the triangle:
Base = 8x = 8 * 8 = 64
Height = 5x = 5 * 8 = 40
Therefore, the base of the triangle is 64 units and the height is 40 units.