Question

If triangle ABC is similar to triangle PQR , area of triangle ABC = 49 sq .units and area of triangle PQR is 81 sq. units AB =7 cm and PQ = ?

Answer 1

PQ = 9 cm

EXPLAINATION

GIVEN

• Area(ΔABC) = 49 sq. unit
• Area(ΔPQR) = 81 sq. unit
• Length of side AB = 7 cm

Theorem

If triangles ABC and PQR are similar triangles, ratio of their area is equal to the square of ratio of their sides.

$\frac{ar(ΔABC)}{ar(ΔPQR)}=(\frac{AB}{PQ})² = (\frac{BC}{QR})² = (\frac{CA}{RP})²$

CALCULATION

From the above theorem,

$\frac{ar(ΔABC)}{ar(ΔPQR)}=(\frac{AB}{PQ})²$

or $\frac{49}{81}=(\frac{7}{PQ})²$

or $\frac{49}{81}=\frac{49}{PQ²}$

or $PQ² = 81$

or $PQ = 9 cm$