Question

20/26
$a^{2}+b^{2}=c^{2}$
$b = 35$ $c = 37$
$a = 11$
$a = 14$
$a = 18$
$a = 12$

Explanation:

Step1: Substitute values into formula

Given $a^{2}+b^{2}=c^{2}$, $b = 35$, $c = 37$. Substitute $b$ and $c$: $a^{2}+35^{2}=37^{2}$.

Step2: Calculate squares

$35^{2}=1225$, $37^{2}=1369$. So the equation becomes $a^{2}+1225 = 1369$.

Step3: Solve for $a^{2}$

Subtract 1225 from both sides: $a^{2}=1369 - 1225=144$.

Step4: Solve for $a$

Take the square - root of both sides. Since we are likely dealing with a geometric context (length), we consider the positive square - root. $\sqrt{a^{2}}=\sqrt{144}$, so $a = 12$.

Answer:

$a = 12$