Step-by-step explanation:
Let the base be x and the perpendicular be y.
It is given that, one leg of a right triangle is twice as long as the other leg,
y = 2x ...(1)
Hypotenuse, H = 5 cm
We can use Pythagoras theorem as follows :
[tex]H^2=B^2+P^2[/tex]
Putting all the values,
[tex]5^2=x^2+(2x)^2\\\\25=x^2+4x^2\\\\25=5x^2\\\\x^2=5\\\\x=\sqrt{5}\ cm[/tex]
So, the base is [tex]\sqrt5\ cm[/tex]. No, to find the value of y put x in equation (1). So,
[tex]y=2x\\\\=2\sqrt{5} \ cm[/tex]
Hence, the measure of the shorter leg is [tex]\sqrt{5} \ cm[/tex]
