Answer: (√10)*a
Step-by-step explanation:
In a triangle rectangle, we have 3 sides, in this case, the shorter base, a, the longer base, b and the hypotenuse h.
And the hypotenuse can be found with the Pythagorean's theorem.
a^2 + b^2 = h^2
now, we know that b = 3a, then we can replace it in the above equation:
a^2 + (3*a)^2 = h^2
a^2 + 9*a^2 = h^2
10*a^2 = h^2
now we can apply the square root to both sides and get:
√(10*a^2) = √h^2
(√10)*a = h
Then we have found the length of the hypotenuse in terms of the shorter side a.
