Video Transcript
Determine the area of the isosceles
triangle ๐ด๐ต๐ถ, given that ๐ด๐ต equals ๐ด๐ถ, ๐ด๐ท is perpendicular to ๐ต๐ถ, and
๐ต๐ถ is equal to the square root of 372 plus two centimetres, and ๐ด๐ท is equal to
the square root of 93 minus one centimetres.
First up, letโs write the relevant
information onto our diagram. Well, ๐ด๐ต equals ๐ด๐ถ has already
been included for us. ๐ด๐ท being perpendicular to ๐ต๐ถ
has also been included for us. So letโs just mark on these
lengths. ๐ต๐ถ is equal to the square root of
372 plus two centimetres, and ๐ด๐ท 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 thatโs the calculation weโve got
to do. Okay, letโs multiply out the
parentheses first.
Weโre gonna do root 372 times root
93. Well, that comes out as root 34596,
which is just 186. Then, weโve got root 372 times
negative one, so thatโs negative root 372. Then, weโve got positive two times
root 93 and positive two times negative one.
Well, before we carry on, letโs
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, weโve 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, Iโve just got 186 minus two, which is 184. And a half of 184 is 92. And donโt 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.
