The height and base of a triangle are in ratio 1:3 respectively. If the area of the triangle is 216 cm\(^2\), find the length of the base.
Question 1 Report
The height and base of a triangle are in ratio 1:3 respectively. If the area of the triangle is 216 cm\(^2\), find the length of the base.
Answer Details
We know that the area of a triangle is given by the formula:
Area = (1/2) x base x height
Let the height of the triangle be h and the base be b. We are given that h:b = 1:3, which means that h = (1/3)b.
Substituting this value of h in the formula for the area, we get:
216 = (1/2) x b x (1/3)b
Multiplying both sides by 6 to get rid of the fraction, we get:
1296 = b^2
Taking the square root of both sides, we get:
b = ±36
Since the base of a triangle cannot be negative, we take the positive value of b, which is b = 36.
Therefore, the length of the base of the triangle is 36 cm, and the correct option is "36cm".
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