Question

if smallest side a right angled triangle is 8. find the two sides​

Answer 1

Step-by-step explanation:

The sequence is 8, 8+x, 8+2x. In a right traingle the squer on the hypotness is equal to the sum of th squers on the other two sides. The hypotness is the longest side => (8+2x)^2 = (8+x)^2 +8^2 = 4x^2 + 2*8*2x + 8^2 = 8^2 + x^2 + 2*8x + 8^2 = 4x^2 + 32x = x^2 + 16x + 64 =>3x^2 + 16x=64 => x^2 + (16/3)*x- 64/3 = 0 => x^2 + (16/3)*x + (8/3)^2 -(8/3)^2 -64/3 = 0 => (x + 8/3)^2 = 64/9 + 64/3 = (64+ 64*3)/ 9 => (x+8/3)^2 = (64+192)/9 = 256/9

=> x+8/3 = sqrt (256/9)

=> x = -8/3 + 16/3 or - 8/3–16/3

=> 8/3 or -8 so (x = 8/3) is the solution

the sides are 8, 8+8/3, 8+16/3

= 8, 32/3, 40/3.

The lengths of the other two sides are

(32/3)Centimeters and (40/3)Centimeters.