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If the sides are in the ratio of 11:16:24, it means that they are all multiples of a same number x, according to these factors.
So, the shorter side is 11x feet long, the middle one is 16x feet long, and the longest side is 24x feet long.
This means that the perimeter is
feet long. But we know that this is 510 feet, so we have
.
So, the three sides are 110, 160 and 240 feet long.
To find the area of a triangle knowing its three sides, you can use Heron's formula, which states that, if is half the perimeter of the triangle whose sides are
, the area
is given by
In our case, so the formula becomes
A graph of the equation shows the appropriate choice to be
C. 2
_____
If you would rather, you can look at the value of the discriminant. For the equation y = ax²+bx+c, the discriminant (d) is
d = b²-4ac
For your equation, this evaluates to
d = (-8)²-4(2)(5) = 64 -40 = 24
When the discriminant is positive, the function has two real roots (2 x-intercepts). When it is zero, there is only one x-intercept, and when it is negative, there are none (the roots are complex).
C. 2
_____
If you would rather, you can look at the value of the discriminant. For the equation y = ax²+bx+c, the discriminant (d) is
d = b²-4ac
For your equation, this evaluates to
d = (-8)²-4(2)(5) = 64 -40 = 24
When the discriminant is positive, the function has two real roots (2 x-intercepts). When it is zero, there is only one x-intercept, and when it is negative, there are none (the roots are complex).