Answer:
[tex]\Huge\boxed{x=7}[/tex]
Step-by-step explanation:
Hello there!
The first thing we want to do is find the measure of the large leg
To do so we use the Pythagorean theorem which says [tex]a^2+b^2=c^2\\[/tex]
where a and b are legs and c is the hypotenuse
we want to find b given the hypotenuse and short leg
so [tex]b^2=c^2-a^2[/tex]
all we have to do is plug in a ( a = short leg so a would equal 12) and c ( c = hypotenuse so c would equal 37)
so
[tex]b^2=37^2-12^2\\37^2=1369\\12^2=144\\1369-144=1225\\b^2=1225\\\sqrt{b^2} =b\\\sqrt{1225} =35\\b=35[/tex]
so the longer leg is equal to 35
35=5x
divide each side by 5
5x/5=x
35/5=7
we're left with x=7
