Answer:
The length of the longest side is 13.33
The length of the other side is 10.67
Step-by-step explanation:
Here we have the lengths of the other two sides will form an arithmetic sequence as follows
[tex]a_n = a_1 + (n-1)d[/tex]
Therefore, the three sides will be of the form
a₁, a₁+d, a₁+2·d
However, we note that the smallest side is a₁ ∴ a₁ = 8
Hence, we have;
8, 8 + d, 8 + 2·d
Also the qustion notes that the triangle is a right angled triange, therefore, Pythagorean equation applies.
Pythagorean equation is
a² + b² = c²
Where:
c = The hypotenuse (the longest side) of the right triangle
Therefore
(8 + d)² + 8² = (8 + 2·d)²
Hence;
d²+16·d+128 = 4·d²+32·d·64
Which gives;
3·d²+16·d-64 =0
Factorizing, we get;
(3·d - 8)(d + 8) = 0
Therefore, d = -8 or d = 8/3
Since, d is a measured increase, therefore, d = 8/3
The other two sides are;
8 + 8/3 = 32/3 = [tex]10\tfrac{2}{3}[/tex] and 8+2×8/3 = 40/3 = [tex]13\tfrac{1}{3}[/tex]
Hence the length of the longest side = [tex]13\tfrac{1}{3}[/tex] = 13.33
The length of the other side = [tex]10\tfrac{2}{3}[/tex] = 10.67.
