Question

what values of a and b make (\triangle ghicong\triangle wvx)?

Explanation:

Step1: Set up equations from congruent sides

Since \(\triangle GHI\cong\triangle WVX\), corresponding sides are equal. So, \(10a=a + 36\) (hypotenuse - hypotenuse) and \(b + 12=5b\) (leg - leg).

For \(10a=a + 36\):

Subtract \(a\) from both sides:
\(10a-a=a + 36-a\)
\(9a=36\)
Divide both sides by \(9\):
\(a=\frac{36}{9}=4\)

For \(b + 12=5b\):

Subtract \(b\) from both sides:
\(b+12 - b=5b - b\)
\(12 = 4b\)
Divide both sides by \(4\):
\(b=\frac{12}{4}=3\)

Answer:

\(a = 4\), \(b = 3\)