+312 A triangle with sides 3a - 1, a2 + 1, and a2 + 2 has a perimeter of 16 units. What is the number of square units in the area of the triangle? I already know the value of a is 2 or -3.5
+129852 We have that
( 3a - 1) + (a^2 + 1) + (a^2 + 2) = 16 simplify
2a^2 + 3a + 2 = 16
2a^2 + 3a - 14 = 0 factor
(2a + 7) ( a - 2) = 0
Only the second linear factor produces a positive for a....
a - 2 = 0
a = 2
So....the sides of the triangle are
3(2) - 1 = 5
2^2 + 1 = 5
2^2 + 2 = 6
The semi-perimeter, s, = [ 5 + 5 + 6 ] /2 = 8
We can find the area by the use of something known as Heron's Formula :
√ [ s ( s - 5) (s - 5) (s - 6) ] =
√ [ 8 * 3 * 3 * 2 ] =
√ [16 * 9 ] =
√144 =
12 units^2
+129852 THX, Mathleteig !!!
We wouldn't necessarily have to use Heron's Formula......
Note that this is an isosceles triangle with a base of 6 and sides of 5
The altitude = √ [side ^2 - (base /2)^2 ] = √ [ 5^2 - 3^2 ]
So....the area is......
(1/2) base * height
(1/2) 6 * √[5^2 - 3^2 ] =
3 * √16 =
3 * 4 =
12 units^2
