A plan of a compound is drawn on a scale of 1cm to 5cm . A. If a wall is 24cm long, find its length on the drawing. B. If the scale drawing of a round house is a circle of diameter 0.7cm,find the actual diameter of the round house?.

2 Answers
Feb 19, 2018

Is everything meant to be in centimetres. That's a very small house and wall! Did you mean 1 centimetre to 5 metres?

Part A: Wall length on the drawing is 5 cm

Part B: The actual diameter of the round house is 3.5 cm ???????

Explanation:

#color(blue)("Defining initial condition")#

Using ratio in fraction FORMAT (this is not a fraction of the whole)

#("length on drawing")/("actual length of object") ->("1 cm")/("5 cm")#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answer for part A")#

Given: The actual wall is 25 cm long

Let the unknown drawing length be #x#

#color(green)(("length on drawing")/("actual length of object") ->("1 cm")/("5 cm") -=x/25)#

Multiply both sides by #color(red)(25)#

#color(green)(1/5 color(red)(xx25)color(white)("d") =color(white)("d")x/25color(red)(xx25))#

#color(green)(color(white)("dd")(color(red)(25))/5color(white)("d.d") =color(white)(".d")x xxcolor(red)(25)/25 )#

But #25/25=1 and 1 xx x =x#

#color(green)(color(white)("dddd")color(white)("d")5color(white)("d")=color(white)("d")x)#

Wall length on the drawing is 5 cm
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answer for part B")#

#color(green)(("length on drawing")/("actual length of object") ->("1 cm")/("5 cm") -=0.7/x)#

For convenience turn every thing upside down so that the #x# is on top.

#color(green)(("actual length of object")/("length on drawing") ->("5 cm")/("1 cm") -=x/0.7)#

Multiply both sides by #0.7#

#color(green)(3.5color(white)(".")cm = x)#

The actual diameter of the round house is 3.5 cm ???????

Feb 19, 2018

Length of wall in drawing plan is #4.8# cm. and
actual diameter of round house is
# 3.5# cm.

Explanation:

Drawing scale : #s=1/5=0.2#. Actual length of wall is #l=24# cm.

Length of wall in drawing plan is #l_d=l*s=24*0.2=4.8# cm.

Round house diameter in the plan of drawing is #d_d=0.7# cm

then , actual round house diameter is #d=d_d/s=0.7/0.2=3.5# cm.

Length of wall in drawing plan is #4.8# cm. and actual diameter

of round house is # 3.5# cm. [Ans]

Remarks: Too small round house and wall , It may be a replica.