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Dennis_Churaev [7]
3 years ago
8

A written explanation solving the question how much fluid is needed using the Pythagorean method and finding the area of the tri

angle

Mathematics
1 answer:
Alecsey [184]3 years ago
6 0

Answer:

793 liters of washing fluid is needed

Step-by-step explanation:

step 1

Find the slant height of the triangular faces of pyramid

we know that

The lateral area of a square pyramid is equal to the area of its four triangular faces

so

LA=4[\frac{1}{2}bl]

where

b is the base of triangle (is the same that the length of the square base)

l is the slant height  

To find out the slant height we need to apply the Pythagorean Theorem

so

l^2=(b/2)^2+h^2

we have

b=35.42\ m

h=21.64\ m

substitute

l^2=(35.42/2)^2+21.64^2

l^2=781.9337

l=27.96\ m

step 2

Find the lateral area of the pyramid

LA=4[\frac{1}{2}bl]

we have

l=27.96\ m

b=35.42\ m

substitute

LA=4[\frac{1}{2}(35.42)(27.96)]

LA=1,980.6864\ m^2

step 3

Find out how much window washing fluid is needed

we know that

2 L of washing fluid cover 5 square meters

so

using proportion

\frac{2}{5}\ \frac{L}{m^2}=\frac{x}{1,980.6864}\ \frac{L}{m^2}\\\\x=1,980.6864(2)/5\\\\x= 792.27\ L

Round up

793 liters of washing fluid is needed

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