Question

1. 12 in 13 in x 5 11. 1 point 34 yd 16 yd b 30 back next page 3 of 4 never submit passwords through google forms. this content is neither created nor endorsed by google. contact form owner - terms of service

Explanation:

Step1: Apply Pythagorean theorem for first triangle

For a right - triangle with sides \(a\), \(b\), and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). In the first triangle with \(a = 12\), \(c = 13\), we want to find the other leg \(x\). So \(x=\sqrt{c^{2}-a^{2}}\).
\[x=\sqrt{13^{2}-12^{2}}=\sqrt{(13 + 12)(13 - 12)}=\sqrt{25\times1}=5\text{ in}\]

Step2: Apply Pythagorean theorem for second triangle

In the second right - triangle with \(a = 16\), \(c = 34\), and we want to find the other leg \(b\). So \(b=\sqrt{c^{2}-a^{2}}\).
\[b=\sqrt{34^{2}-16^{2}}=\sqrt{(34 + 16)(34 - 16)}=\sqrt{50\times18}=\sqrt{900}=30\text{ yd}\]

Answer:

For the first triangle, \(x = 5\) in. For the second triangle, \(b = 30\) yd.