If the 3 sides of a triangle have lengths 9m, 12m, and 15m, what is the area of this triangle?
therefore since the scale ration is 4/1, the ratio of areas is 16 to 1
16* 6 = 96
Whoops, sorry, 3/1
9*6 = 54
or just brute force do
(1/2)(12)(9) = 6*9 = 54
To find the area of the triangle, we can use Heron's formula. Heron's formula states that the area of a triangle with side lengths a, b, and c can be calculated using the formula:
area = sqrt(s * (s - a) * (s - b) * (s - c))
where s is the semi-perimeter of the triangle and is calculated using the formula:
s = (a + b + c) / 2
Let's calculate the area step by step:
1. First, calculate the semi-perimeter (s) of the triangle:
s = (9m + 12m + 15m) / 2
= 36m / 2
= 18m
2. Next, use the semi-perimeter (s) to calculate the area:
area = sqrt(18m * (18m - 9m) * (18m - 12m) * (18m - 15m))
= sqrt(18m * 9m * 6m * 3m)
= sqrt(2916m^4)
= 54m^2
Therefore, the area of the triangle with side lengths 9m, 12m, and 15m is 54 square meters.
that is a 3,4,5 right triangle (25 = 9+16)
therefore if we take 4 as the base, 3 is the altitude
(1/2) b h = (1/2)(4)(3) = 6