Mathematics Question and Solution
Calculating Area Triangle ABC.
Let a be the height of the triangle.
b = √(a²+4) units.
b is AC.
c = √(a²+9) units.
c is BC.
Calculating a.
½(2+3)a = ½√(a²+4)*√(a²+9)sin45
10a = √(2(a²+4)(a²+9))
100a² = 2a⁴+26a²+72
2a⁴-74a²+72 = 0
a⁴-37a²+36 = 0
a⁴-a²-36a²+36 = 0
a²(a²-1)-36(a²-1) = 0
(a²-1)(a²-36) = 0
It implies;
a² = 1 or a² = 36
Therefore;
a ≠ √(1) units.
a = √(36)
a = 6 units.
Area Triangle ABC is;
½*a*(AB)
= ½*6*(2+3)
= 3(5)
= 15 square units.
