Question

What is the answer??

Answer 1

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

`x=(-b+√(D))/(2a) \ or \ x =(-b-√(D))/(2a)\\\\x= (-8+24.16)/(2*2) \ or \ x = (-8-24.6)/(2*2)` {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 =
`(1)/(2)* base * height`

`=(1)/(2)*4.04 *8.04\\\\= 2.02 * 8.04`

= 16.24 sq.cm