The base and height of a triangle are in the ratio 5:3.if the area of the triangle is 67.5 square metre.find its base and height.
A = b*h/2,
A = 5x * 3x / 2 = 67.5,
Multiply both sides by 2:
5x * 3x = 135,
15x^2 = 135,
x^2 = 9,
X = 3.
b = 5x = 5*3 = 15.
h = 3x = 3*3 = 9.
To find the base and height of the triangle, we can use the formula for the area of a triangle:
Area = (base * height) / 2
Given that the area is 67.5 square meters and the base and height are in a ratio of 5:3, we can set up an equation to solve for the base and height.
Let's represent the ratio as 5x and 3x, where x is a common factor.
So, the formula for the area becomes:
67.5 = (5x * 3x) / 2
To simplify the equation, we multiply 5x with 3x and divide it by 2:
67.5 = (15x^2) / 2
To solve the equation, we can multiply both sides by 2 to eliminate the fraction:
2 * 67.5 = 15x^2
135 = 15x^2
Divide both sides by 15:
135 / 15 = 15x^2 / 15
9 = x^2
Taking the square root of both sides:
√9 = √(x^2)
3 = x
Since x represents the common factor, we can find the base and height by multiplying 5 and 3 by 3:
Base = 5x = 5 * 3 = 15
Height = 3x = 3 * 3 = 9
Therefore, the base of the triangle is 15 meters and the height is 9 meters.