Question

Given triangle ABC is similar to triangle PQR, if the ratio of area triangle ABC to area triangle PQR is 121:225, then find the ratio of PR to AC​

Answer 1

Given:

• Triangle ABC is similar to triangle PQR,
• The ratio of area triangle ABC to area triangle PQR is 121:225

To find:

The ratio of PR to AC

Form a theorem:

The ratio of the areas of two similar triangles is equivalent to the ratio of the squares of their corresponding sides.

So,

$\dfrac{121}{225} = (\dfrac{PR}{AC})^{2}$

$\implies (\dfrac{11}{15})^{2} = (\dfrac{PR}{AC})^{2}$

$\implies (\dfrac{11}{15})= (\dfrac{PR}{AC})$

Hence,e

The ratio of PR to AC is 11:15

More Information

• In such a similar question, when the side ratio is given and the ratio of the area of the triangle is asked then square the given side ratio.
• When the ratio of the area of the similar triangle is given and the question asked to find the ratio of sides then take out the square root of the ratio of the area of the triangles.

Answer 2

Answer:

Given :-

∆ABC = ∆PQR

Ratio of two areas = 121:225

To Find :-

Ratio of PR to AC

Solution :-

According to the question

Ratio of areas = square of the given sides

So,

$\bigg(\dfrac{121}{225}\bigg) = \sf {\bigg(\dfrac{AC}{PR}\bigg)}^{2}$

√121 = 11

√225 = 15

$\sf\dfrac{11}{15} = \dfrac{AC}{PR}$