Solution,
Given:
Area of the rectangular faces of a prism (L.S.A) = 180 cm2., ∠PQR = 90°, PR = 5cm
To find:
The length of PP'
Here, PQ = P'Q' = 3cm
Then, in the right angles triangle PQR,
PQ2 + QR2 = PR2
Or, (3cm)2 + QR2 = (5cm)2
Or, 9cm2 + QR2 = 25cm2
Or, QR2 = 16cm2
Or, QR = 4cm
Again,
Perimeter of triangle PQR = PQ + QR + PR
= 3 cm + 4 cm + 5 cm
= 12 cm
Now, by formula
L.S.A of a prism = perimeter of the base x height
Or, 180 cm2 = 12 x PP'
Or, \(\frac{180cm^2}{12cm}=PP'\)
Or, 15 cm = PP'
∴ The length of PP' = 15 cm