Question 2.2. The height of a triangle is 5 m less than its base. The area of the triangle is 42 m2. Find the length of the base.
(Points : 1)
12 m
11 m
8 m
7 m
i think it's 12m
You are correct, since 12*7/2 = 42.
To find the length of the base of the triangle, we can use the formula for the area of a triangle, which is given by:
Area = (1/2) * base * height
In this case, we are given that the height of the triangle is 5 m less than its base. Let's call the length of the base "x". So, the height would be "x - 5".
Now, we can substitute these values into the area formula:
42 = (1/2) * x * (x - 5)
Simplifying this equation, we get:
42 = (1/2) * (x^2 - 5x)
Multiplying both sides of the equation by 2 to remove the fraction, we have:
84 = x^2 - 5x
Rearranging the equation to form a quadratic equation:
x^2 - 5x - 84 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula. By factoring, we find:
(x - 12)(x + 7) = 0
This gives us two possible solutions: x = 12 or x = -7.
Since the length of the base cannot be negative, we ignore the solution x = -7.
Therefore, the length of the base of the triangle is 12 m. So, the correct answer is 12 m.