1.
The side lengths are in the ratio 11:16:24, so let them be
11k, 16k, and 24k for some number k.
11k+16k+24k=510
k(11+16+24)=510
51k=510
k=10
so the actual sides are 110, 160 and 240 feet.
2.
There is a famous formula, called Heron's formula, which calculates the area of a triangle, given its sides a, b and c.
we first calculate the half perimeter, which we usually denote by u:
[tex]u= \frac{a+b+c}{2} [/tex]
then the theorem states that the area A is as follows:
[tex]A= \sqrt{u(u-a)(u-b)(u-c)} [/tex]
3.
In our case:
[tex]u= \frac{a+b+c}{2} =\frac{110+160+240}{2} = \frac{510}{2} [/tex]
[tex]u-a= \frac{510}{2} -110= \frac{510-220}{2} = \frac{290}{2} [/tex]
[tex]u-b= \frac{510}{2} -160= \frac{510-320}{2} = \frac{190}{2} [/tex]
[tex]u-a= \frac{510}{2} -240= \frac{510-480}{2} = \frac{30}{2} [/tex]
[tex]A= \sqrt{\frac{510}{2}*\frac{290}{2}* \frac{190}{2} * \frac{30}{2}} =7,258.745[/tex] feet squared
Answer:D 7,258.745 ft squared
