Question

3. The sides of a right-angled triangle ar
(x - 1) cm, 3x cm and (3x + I) cm. Find :
(i) the value of x,
(ii) the lengths of its sides,
(iii) its area.​

Answer 1

Step-by-step explanation:

i. Using Pythagoras Theorem

Hypotenuse^2 = Altitude^2 + Base^2

(3x+1)^2 = (3x)^2 + (x-1)^2

9x^2 +1 +6x = 9x^2 +x^2 +1 - 2x

8x = x^2

x^2-8x = 0

x(x-8)=0

Hence, x=0 or x = 8

Putting x= 0 will negative values hence it cannot form triangle

So x=8 is the right answer

ii.

Lengths of sides

x-1 = 8-1 = 7

and 3x = 3*8 = 24

and 3x+1 = 3*8+1 = 25 (Hypotenuse)

iii. Area of right angle triangle, A = 1/2(Base * Altitude)

A = 1/2(7*24) = 84