Question

PQRS is rectangle. T is a point on PQ such that RTQ is an isosceles triangle and PT = 5QT. if the area of ∆RTQ is 12√3 sq. cm, then area of rectangle PQRS is:​

Answer 1

Step-by-step explanation:

RTQ is an isosceles triangle and PT = 5 QT.

So if QT = 1 cm then PT = 5 cm

⇒ TR divides the line PQ in the ratio 1 : 5 ……… ( TQ : PT ) = 1 : 5

Then the area of triangles divided by TR will be in the ratio 1 : 5

If the area RTQ = 12√3 sq.cm

Then area RTP = 5 × 12√3 = 60√3

Hence ar( PRQ) = 12√ 3 + 60√ 3 = 72√ 3

PR is diagonal which divides PQRS in two equal areas .

So ar PQRS = 2× 72 √3 = 144√3 cm^२

I hope it's helpful to u