Question

what values of s and t make (\triangle efgcong\triangle jik)?

Explanation:

Step1: Set up equations based on congruent triangles

Since \(\triangle EFG\cong\triangle JIK\), corresponding sides are equal. So we have \(3s + 5=s + 43\) (for the non - hypotenuse sides) and \(3t=5t - 38\) (for the hypotenuse sides).

Solve for \(s\):

Step2: Isolate \(s\) in \(3s + 5=s + 43\)

Subtract \(s\) from both sides: \(3s - s+5=s - s + 43\), which gives \(2s+5 = 43\).
Subtract \(5\) from both sides: \(2s+5 - 5=43 - 5\), so \(2s=38\).
Divide both sides by \(2\): \(s=\frac{38}{2}=19\).

Solve for \(t\):

Step3: Isolate \(t\) in \(3t=5t - 38\)

Subtract \(3t\) from both sides: \(3t-3t = 5t-3t - 38\), which gives \(0 = 2t-38\).
Add \(38\) to both sides: \(38=2t\).
Divide both sides by \(2\): \(t = 19\).

Answer:

\(s = 19\), \(t = 19\)