Question

If triangle ABC ~Triangle QRP ,ar(ABC)÷ar(QRP)=9÷4 and BC=15cm then find PR

Answer 1

so the answer for this question is :PR=10cm.
i hope this answer will be helpful for you

Answer 2

Answer: PR = 10 cm

Step-by-step explanation:

If the two triangles are similar then all corresponding sides are in the same proportion,

While the ratio of their area is equal to the square of this proportion,

Here, triangle ABC and QRP are similar,

Thus, by the above property,

$\frac{ar(\triangle ABC)}{ar(\triangle QRP)}=(\frac{BC}{PR})^2$

⇒ $\frac{9}{4}=(\frac{15}{PR})^2$

⇒ $\frac{3}{2}=(\frac{15}{PR})$

⇒ $3 PR = 15\times 2$

⇒ $3PR = 30$

⇒ $PR=10$

Hence, the measurement of segment PR = 10 cm.