Question

Can three line segments with the given lengths form a right triangle?

Answer 1

Answer:

Yes

12, 35, 37

16, 30, 34

20, 21, 29

No

18, 24, 42

Step-by-step explanation:

Required

Determine which length form a right triangle

To do this, we make use of Pythagoras theorem where the square of the largest length = the sum of the squares of the other lengths

So:

(1) 12, 35, 37 --- Yes

$37^2 = 35^2 + 12^2$

$1369 = 1225 + 144$

$1369 = 1369$

(2) 16, 30, 34 --- Yes

$34^2 = 16^2 + 30^2$

$1156 = 256 + 900$

$1156 = 1156$

(3) 18, 24, 42 --- No

$42^2 =18^2 + 24^2$

$1764 =324 + 576$

$1764 =900$

$1764 \ne 900$

(4) 20, 21, 29 -- Yes

$29^2 = 20^2 + 21^2$

$841= 400 + 441$

$841= 841$