Question

exercises: find the length of the hypotenuse in the following triangles
use the formula ( c^{2}=a^{2}+b^{2} )
1)
2)
3)
4)

Explanation:

Step1: Substitute values into formula

For the first triangle:
$$c^{2}=9^{2}+12^{2}$$
$$c^{2}=81 + 144$$
$$c^{2}=225$$
$$\sqrt{c^{2}}=\sqrt{225}$$
$$c = 15$$

For the second triangle:
$$c^{2}=5^{2}+12^{2}$$
$$c^{2}=25+144$$
$$c^{2}=169$$
$$\sqrt{c^{2}}=\sqrt{169}$$
$$c = 13$$

For the third triangle:
$$c^{2}=9^{2}+40^{2}$$
$$c^{2}=81 + 1600$$
$$c^{2}=1681$$
$$\sqrt{c^{2}}=\sqrt{1681}$$
$$c = 41$$

For the fourth triangle:
$$c^{2}=24^{2}+7^{2}$$
$$c^{2}=576+49$$
$$c^{2}=625$$
$$\sqrt{c^{2}}=\sqrt{625}$$
$$c = 25$$

Answer:

1. \(c = 15\) in.
2. \(c = 13\) in.
3. \(c = 41\) cm.
4. \(c = 25\) cm.