Question

Finding Leg Lengths. Find the length of a leg in the 45°-45°-90° triangle.

Answer 1

Answer:

12. $x=10$

13. $x=4$

14. $x=5$

15. $x=1$

16. $x=8$

17. $x=14$

Step-by-step explanation:

for these i also used the pythagorean theorem ($a^{2}+b^{2}=c^{2}$)

$a$ and $b$ are the legs, $c$ is the hypotenuse

12.

$x^{2} +x^{2} =(10\sqrt{2} )^{2}$

$2x^{2} =200$

$x^{2} =100$

$x=10$

13.

$x^{2} +x^{2} =(4\sqrt{2} )^{2}$

$2x^{2} =32$

$x^{2} =16$

$x=4$

14.

$x^{2} +x^{2} =(5\sqrt{2} )^{2}$

$2x^{2} =50$

$x^{2} =25$

$x=5$

15.

$x^{2} +x^{2} =(\sqrt{2} )^{2}$

$2x^{2} =2$

$x^{2} =1$

$x=1$

16.

$x^{2} +x^{2} =(8\sqrt{2} )^{2}$

$2x^{2} =128$

$x^{2} =64$

$x=8$

17.

$x^{2} +x^{2} =(14\sqrt{2} )^{2}$

$2x^{2} =392$

$x^{2} =196$

$x=14$