Answer:
= 6 square unit
Step-by-step explanation:
Area of a triangle is 1/2 × base × height
first we find CD
we use Pythagoras theorem
we represent CD with x
3² = 1.8² + x²
9 = 3.24 + x²
x² = 9 - 3.24
x² = 5.76
x = √5.76
x = 2.4
so
CD = 2.4
Area of a triangle = 1/2 × base × height
According to ∆ABC,
AB² = AC²+BC²
Since AB = AD+DB then;
(AD+DB)² = AC²+BC²
AD² + 2(AD)(DB)+DB² = AC²+BC²
DB² = AC²+BC² - AD² - 2(AD)(DB)... 1
According to ∆BCD
BC² = CD²+DB²
DB² = BC²-CD²...2
Equating 1 and 2
AC²+BC² - AD² - 2(AD)(DB) = BC²-CD²
AC² - AD² - 2(AD)(DB) + CD² = 0
AC = 3
AD = 1.8
CD = 2.4
On substituting
3²-1.8² - 2(1.8)DB +2.4² = 0
9-3.24-3.6DB+5.76 = 0
11.52 - 3.6DB = 0
3.6DB = 11.52
DB = 11.52/3.6
DB = 3.2
The base of the triangle
AB = AD+DB
AB = 1.8+3.2
AB = 5.0
Area of the triangle = 1/2 × 2.4 × 5
= 1.2 × 5
= 6 square unit
