Question

area of the east wall of auditorium is 108 sq m. area of the north wall is 135 sq m and area of the floor is 180 sq m. find the height of the auditorium.

Answer 1

Hi,

Dimensions of the auditorium are ,

i ) east side wall

Length = l

Height = h

Area = 108 sq m

lh= 108

h = 108 / l -------( 1 )

ii ) north wall ,

length = b

Breadth = h

Area = 135 sq m

bh = 135

h = 135 / b-------( 2 )

iii ) floor dimensiins ,

Length = l

Breadth = b

Area = 180 sq m

lb = 180

b = 180 / l --------( 3 )

We observe that ,

( 1 ) = ( 2 )

108 / l = 135 / b

b = ( 135 × l ) / 108

b = ( 5 / 4 ) l ------( 4 )

( 3 ) = ( 4 )

180 / l = ( 5 / 4 ) l

( 180 × 4 ) / 5 = l^2

36 × 4 = l^2

144 = l^2

Therefore ,

l = 12 m

Put l = 12 m in equation ( 1 )

h = 108 / 12

h = 9 m

Therefore ,

Height of the auditorium = h = 9 m

I hope this helps you.

:)