Question

The ratio of sides of two similar triangles is 14:11, then the ratio of area of two triangle is

Answer 1

Answer:

The ratio of area of triangles  is $\dfrac{196}{121}$  .

Step-by-step explanation:

Given as :

The ratio of sides of similar triangle = 14 : 11

Let The ratio of area of triangles = ar ΔABC : ar ΔPQR

Let The two triangle = Δ ABC , Δ PQR

And Δ ABC ≈ Δ PQR

Let $\dfrac{AB}{PQ}$  = $\dfrac{14}{11}$

From the property of similar triangle

$\dfrac{ar \Delta ABC}{ar\Delta PQR}$ = ( $\dfrac{AB}{PQ}$ ) ²

Or, $\dfrac{ar \Delta ABC}{ar\Delta PQR}$ = $(\dfrac{14}{11})^{2}$

Or, $\dfrac{ar \Delta ABC}{ar\Delta PQR}$ = $\dfrac{196}{121}$

So, The ratio of area of triangles = $\dfrac{ar \Delta ABC}{ar\Delta PQR}$ = $\dfrac{196}{121}$

Hence, The ratio of area of triangles  is $\dfrac{196}{121}$  . Answer