Question

what values of s and t make $\triangle hij \cong \triangle wxv$?

work it out
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Explanation:

Step1: Match congruent hypotenuses

Set $HI = XW$:
$s + 32 = 5s$

Step2: Solve for $s$

Rearrange and simplify:
$32 = 5s - s$
$32 = 4s$
$s = \frac{32}{4} = 8$

Step3: Match congruent legs

Set $HJ = WV$:
$s - 3t + 40 = t - 5s + 48$

Step4: Substitute $s=8$ and solve for $t$

Substitute $s=8$:
$8 - 3t + 40 = t - 5(8) + 48$
$48 - 3t = t - 40 + 48$
$48 - 3t = t + 8$
$48 - 8 = t + 3t$
$40 = 4t$
$t = \frac{40}{4} = 10$

Answer:

$s = 8$
$t = 10$