Question

IF AREA IF TRIANGLE ABC ~ AREA OF TRIANGLE PQR and 4A(AABC) = 25 A(APQR), then AB : PQ = ?
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Answer 1

Answer:4 A(TriangleABC)=25 A(TrianglePQR)

i.e A(ABC):A(PQR)=25:4

Therfore, By Area side relationship of similar Triangles

Side of ABC ÷Side of PQR = underroot o[ A(ABC): A(PQR)

ie AB:PQ=5:2

Step-by-step explanation:

Answer 2

AB : PQ = 5:2

Step-by-step explanation:

If $ar(\bigtriangleup ABC) \sim ar(\bigtriangleup PQR)$

then

Theorem: If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

here ,

$\frac{4 ar(\bigtriangleup ABC)}{25 ar(\bigtriangleup PQR)} = \frac{AB^2}{PQ^2}$...(1)

i.e

$\frac{ar(\bigtriangleup ABC)}{ ar(\bigtriangleup PQR)} = \frac{25}{4}$..(2)

using 1 and 2

$\frac{AB^2}{PQ^2} = \frac{25}{4} \\\frac{AB}{PQ} = \sqrt{ \frac{25}{4}} \\\frac{AB}{PQ} = \frac{5}{2}$

Hence ,

AB :PQ = 5:2

#Learn more:

Area of AABC = 36 and area of APQR = 64. The correspondence ABC + PQR is a similarity. If

AB= 12, Find PQ.

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