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.
let the base be 5x and the height 3x ,
area of triangle = (1/2)base x height
(1/2)(5x)(3x) = 67.5
35x^2 = 135
x^2 = 9
x = √9 = 3
so base is 5x = 15
height is 3x = 9
check:
15 : 9 = 5 : 3
(1/2)(15)(9) = 67.5
To find the base and height of a triangle when only the ratio of the base and height is given, we need to use the formula for the area of a triangle.
The area of a triangle is given by the formula:
Area = (1/2) * base * height
Given that the area of the triangle is 67.5 square meters, we can substitute this value into the formula:
67.5 = (1/2) * base * height
Next, we are given that the base and height are in the ratio 5:3. We can represent this ratio as:
base = 5x
height = 3x
Substituting these values into the formula, we have:
67.5 = (1/2) * 5x * 3x
Simplifying the equation:
67.5 = (15/2) * x^2
Dividing both sides by 15/2:
x^2 = (2/15) * 67.5
x^2 = 9
Taking the square root of both sides:
x = ±√9
x = ±3
Since we can't have a negative value for the base or height, we take x = 3.
Therefore, the base is 5 * 3 = 15 units and the height is 3 * 3 = 9 units.
Hence, the base of the triangle is 15 units and the height is 9 units.