Question 807423
One of the sides serves as a base and the other side serves as a height.

Area is {{{(1/2)b*y}}}, where b is base, y is height.


{{{(1/2)(5x)(3x-1)=60}}} using what was given.
b=5x and y=3x-1
{{{5x(3x-1)=120}}}
{{{15x^2-5x=120}}}
{{{3x^2-x=24}}}
{{{3x^2-x-24=0}}} FACTORABLE!
{{{(3x+8)(x-3)=0}}}


The positive x value has meaning here.
{{{highlight(x=3)}}}
The triangle legs are {{{5x=5*3=15}}} and {{{3x-1=3*3-1=8}}}


Pythagorean Theorem gives {{{h^2=15^2+8^2}}}
{{{h^2=289}}}
{{{highlight(h=17)}}}



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Knowing the squares of the lowest few prime numbers is a good idea.
11^2=121; 13^2=169; for 17 obviously; 19^2=361.
You'll find that your common divisibility rules give you nothing for 289, so suspect some lower prime number as a possible factor.