Video Transcript
Determine the area of the isosceles
triangle 𝐴𝐵𝐶, given that 𝐴𝐵 equals 𝐴𝐶, 𝐴𝐷 is perpendicular to 𝐵𝐶, and
𝐵𝐶 is equal to the square root of 372 plus two centimetres, and 𝐴𝐷 is equal to
the square root of 93 minus one centimetres.
First up, let’s write the relevant
information onto our diagram. Well, 𝐴𝐵 equals 𝐴𝐶 has already
been included for us. 𝐴𝐷 being perpendicular to 𝐵𝐶
has also been included for us. So let’s just mark on these
lengths. 𝐵𝐶 is equal to the square root of
372 plus two centimetres, and 𝐴𝐷 is equal to the square root of 93 minus one
centimetres.
And also let us recall that the
area of a triangle is equal to half times the base times the perpendicular
height. So the area of a triangle is a half
times the base. Well this is the base, the square
root of 372 plus two, times the perpendicular height; well, this is our
perpendicular height. So that’s the calculation we’ve got
to do. Okay, let’s multiply out the
parentheses first.
We’re gonna do root 372 times root
93. Well, that comes out as root 34596,
which is just 186. Then, we’ve got root 372 times
negative one, so that’s negative root 372. Then, we’ve got positive two times
root 93 and positive two times negative one.
Well, before we carry on, let’s
look at this: the square root of 372. The 372 can be written as four
times 93. And the square root of four times
93 is the same as the square root of four times the square root of 93. And the square root of four is
two. So we can write that as two times
root 93 or just two root 93.
So now, we’ve got 186 take away two
root 93 plus two root 93 take away two. Well, if I start with negative two
root 93 and I add two root 93, those two things are gonna cancel each other out and
make zero. So in the brackets or in the
parentheses, I’ve just got 186 minus two, which is 184. And a half of 184 is 92. And don’t forget that our length
units were centimetres, so the area is gonna be in centimetres squared. So the answer is the area is 92
centimetres squared.
