Answer:
The length of the hypotenuse is 26 cm.
Step-by-step explanation:
In order to find the hypotenuse in this right triangle you can use the Pythagoras' Theorem.
The Pythagorean Theorem tells us that the relationship in every right triangle is:
[tex]a^{2}+b^{2}=c^{2}[/tex],
See the picture attached to know what is the meaning of constants a, b and c.
In the triangle given, a = 24cm and b = 10 cm, now you can use the Pythagorean Theorem to find c or the hypotenuse.
[tex]a^{2}+b^{2}=c^{2}\\ 24^{2}+10^{2}=c^{2}\\ 576+100=c^{2}\\ c^{2}=676\\\mathrm{For\:}x^2=\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{\left(a\right)},\:\:-\sqrt{\left(a\right)}\\ x_{1}=\sqrt{676}, x_{2}=-\sqrt{676} \\ x_{1}=26, x_{2}=-26[/tex]
Because we are finding the distance between points AB, this distance cannot be negative, so the answer is the length of the hypotenuse is 26 cm.
