# In a plan of a house, the width, 150 cm, of a door is represented by a line 30 mm long. Find the area of the house if the corresponding area on the..plan is 3250 cm^2.

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First of all, we must assume what the shape of the house is or else there is no way to know the answer. So I will assume that the house is a rectangle.

We know that the ratio of the actual door to the drawing of it is 50:1. But we can not just multiply the area of the plan by 50. Instead, we must multiply it by 2500 because both the length and width of the house is 5 times greater than what it is on the plan.

So, we multiply 3250*2500.

That gets us 8,125,000 cm^2 for the area of the real house.

The actual length of the door = 150cm. The length of the door on the map = 30mm.

We know that the map is a similar figure to the actual figure on the ground.

The area of similar figures bear the square of any corresponding linear dimensional ratios. So, here, the actual door length and the length of the door on the map are the corresponding linear dimensions of the similar figures. Therefore,

Actual area of the house on the ground /area of the house on the map = square of the actual length of the door/square of the length of the door on the map.

Therefore the actual area of the house = (150cm)^2/(30mm)^2] (area of the house in map)=(150*10mm)^2/(30mm)^2 ](Area of the house in map)

=(1500^2/30^2)(3250cm^2)

=8125000 cm^2

=8125000cm^2/(100cm*100cm) ]m^2

=812.5 m^2

Given:

30 mm on plan = 150 cm actual

Area of plan = 3250 cm^2

Solution:

It is given:

150 cm actual = 30 mm = 30/10 cm = 3 cm

Therefore

I meter actual = 100 cm actual = (3/150)*100 = 2 cm

Therefore:

Area equal to 2 cm by 2 cm on map = 4 cm^2 on map

Will represent an area equal to 1 m by 1 m = 1 m^2 actual

Therefore:1 cm^2 on map = 1/4 m^2

Therefore: 3250 cm^2 on map = 3250*1/4 m^2 = 812.5 m^2

Answer:

Area of the house = 812.5 m^2