Question

in the figure angle PQR is equal to Angle PST equal to 90 degree PQ = 5 cm and PR = 2 cm ​

Answer 1

Answer: 25:21

Step-by-step explanation:

Answer 2

Answer:

Δ PQR ≅ ΔPTS

25:21

Step-by-step explanation:

in Δ PQR & ΔPTS

∠PQR = ∠PST = 90°

∠QPS = ∠TPS =  x° (same Angle)

As sum of three angles of triangle = 180° , Two angles are equal so third angle would also be equal 180°-90°-x° = 90°-x°

∠QRP = ∠PTS = 90°-x°

as all three angle are equal

so

Δ PQR ≅ ΔPTS

so Ratio of Sides = PQ/PS = 5/2 = 2.5

Let Say area of small triangle ΔPTS= x  cm²

Area of similar triangle is in ratio of squares of ratio of their sides

then area of larger triangle Δ PQR = (2.5)²x = 6.25x cm²

Area of Quadrilateral SRQT = Area of Δ PQR - Area of ΔPTS

=> Area of Quadrilateral SRQT = 6.25x - x = 5.25x cm²

Area of Δ PQR : Area of Quadrilateral SRQT :: 6.25x : 5.25x

Area of Δ PQR : Area of Quadrilateral SRQT :: 625 : 525

Area of Δ PQR : Area of Quadrilateral SRQT :: 25 : 21