Question

Show me how to solve it​

Answer 1

Given,

• ΔABC is similar to ΔPQR

• $AC = 4\sqrt{3}, BC = 8, QP = 3, QR = 6$

To find,

$a + b$

Solution,

When two triangles are similar, their sides are in proportion that is,

                         $\frac{AB}{PQ} = \frac{BC}{QR} = \frac{CA}{RP}$

Using,

                   $\frac{AB}{PQ} = \frac{BC}{QR}\\ \frac{b}{3} = \frac{8}{6} \\b = 4$

Similarly using,

                              $\frac{BC}{QR} = \frac{CA}{RP} \\\\\frac{8}{6} = \frac{4\sqrt{3} }{a}\\a = 3\sqrt{3}$

Now, $a + b = 4 + 3\sqrt{3}$

Therefore the value of $a + b$ is $4 + 3\sqrt{3}$.