How should I do this question that is in the image below?50
2 Answers
Second triangular block, by
Explanation:
Well, since they give us only the lengths of the triangle, we will have to use Heron's formula, which states that the length of a triangle is
where
Let
We have:
Next step, let's find
So, the second triangular block has a greater area by
The second block has greater area, by (approximately)
Explanation:
The formula most of us remember for finding triangle area is:
#A=1/2bh#
where
#A=1/2ab sin C#
and
#A=sqrt(s(s-a)(s-b)(s-c))#
where
The formula we use depends on the information we're given. When we know all three sides, as in this example, we can use
For the first triangle:
#s=1/2(a+b+c)#
#color(white)s=1/2(25+48+53)#
#color(white)s=126/2=63 " m"#
So the area of the first triangle, call it
#A_1=sqrt(s(s-a)(s-b)(s-c))#
#color(white)(A_1)=sqrt(63(63-25)(63-48)(63-53))#
#color(white)(A_1)=sqrt(63(38)(15)(10))#
#color(white)(A_1)=sqrt(3*3*7(2*19)(3*5)(2*5))#
#color(white)(A_1)=2*3*5sqrt(7(19)(3))#
#color(white)(A_1)=30sqrt(399)#
#color(white)(A_1)~~599" m"^2#
I'll leave the area of triangle 2 as an exercise. Its value is
After comparing