Answer:
Step-by-step explanation:
Let AC = x
AB - AC = 4 cm
AB = 4 +x ----------------(I)
Pythagorean theorem
AB² + AC² =BC²
(4 + x)² + x² = 9²
Use the identity (a + b)² = a² + 2ab + b² where a = 4 & b = x
4² +2*4*x +x² + x²= 81
16 + 8x + 2x² = 81
2x² + 8x + 16 - 81 = 0
2x² + 8x - 65= 0
a = 2 ; b = 8 ; c = -65
D = b² - 4ac
= 8² - 4*2*(-65)
= 64 + 520
D = 584
√D = √584 = 24.16
{Ignore this as it is negative.}
x = 16.16/4
x = 4.04
AC = 4.04 Cm
AB = 4 + 4.04 = 8.04 cm
Area of triangle ABC =
= 16.24 sq.cm