Question

what values of a and b make $\triangle pqr \cong \triangle vuw$?
(there are two right triangles: $\triangle pqr$ with right angle at p, pq=15, qr=7b; $\triangle vuw$ with right angle at v, vu=5a, uw=42)
$a = \square$
$b = \square$

Explanation:

Step1: Identify corresponding sides

Since $\triangle PQR \cong \triangle VUW$, their corresponding sides are equal. In right triangles, the legs correspond. So, $QP = VU$ and $QR = VW$.
$QP = 15$, $VU = 5a$. So, $5a = 15$.

Step2: Solve for a

Solve the equation $5a = 15$. Divide both sides by 5: $a = \frac{15}{5} = 3$.

Step3: Solve for b

$QR = 7b$, $VW = 42$. So, $7b = 42$. Divide both sides by 7: $b = \frac{42}{7} = 6$.

Answer:

$a = 3$, $b = 6$