Question

find the missing length of the figure. 5 mm 12 mm 35 mm x = □ mm

Explanation:

Step1: Apply Pythagorean theorem

First, find the length of the hypotenuse of the smaller right - triangle with sides 5 mm and 12 mm. Let this hypotenuse be $a$. By the Pythagorean theorem $a^{2}=5^{2}+12^{2}$. So, $a^{2}=25 + 144=169$, and $a = 13$ mm.

Step2: Apply Pythagorean theorem again

Now, consider the larger right - triangle with one side 35 mm and the other side (the hypotenuse of the smaller triangle) 13 mm. Let the missing side be $x$. By the Pythagorean theorem $x^{2}=35^{2}+13^{2}$. Then $x^{2}=1225+169 = 1394$. So, $x=\sqrt{1394}\approx37.3$ mm.

Answer:

$37.3$ mm