Question

In triangle PQR TS || RQ if TP =3cm TR= 2cm SQ = 3 cm find PS

Answer 1

Answer:

here's your solution

Step-by-step explanation:

Given ∆abc

TS||RQ

PS =3cm , SR =4 cm

To find Area of ∆ PST / Area of ∆ PQR

Proof:-

in ∆PQR & PST,

angle QPR = angle TPS

angle PRO =angle PST

∆ PRO ~ ∆ PST

Now,

We know that in similar triangles,

Ratio of area if triangle is equal to the ratio of square of corresponding sides

Area of ∆ PST / Area of ∆ PQR =(PS/PR)²

Area of ∆ PST / Area of ∆ PRQ =(PS / PS +SR)²

Area of ∆ PST / Area of ∆ PQR =(3/3+4)²

Area of ∆ PST / Area of ∆ PRO = (3/7)²

Area of ∆ PST / Area of ∆ PRO = 9 / 49

so therefore the ratio is 9/49

hope it will be helpful to you!!!