Question

Consider the triangle. Find the length of the hypotenuse, c

The length of the hypotenuse is (blank) cm.

Answer 1

The lenght should be 26 cm

Answer 2

The length of the hypotenuse is 26 cm.

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:

`a^(2)+b^(2)=c^(2)`,

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.

`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=√(\left(a\right)),\:\:-√(\left(a\right))\\ x_(1)=√(676), x_(2)=-√(676) \\ x_(1)=26, x_(2)=-26`

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.