3 years ago

A number greater than -5 written as a problem

Mathematics

1 answer:

bazaltina [42]3 years ago

7 0

The answer is x > -5

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1. Consider the pyramid ABCDE in the figure 1 attached:

Each side of the square base equals $\sqrt{20} = \sqrt{4*5} = \sqrt{4}* \sqrt{5}=2 \sqrt{5}$ (units)

Area of 1 lateral side of pyramid ABCDE is $\frac{1}{2}* 2 \sqrt{5}*x=\sqrt{5}x$

so the total lateral area is $4\sqrt{5}x$ (units squared)

and the total surface area is $20+4\sqrt{5}x$ (units squared)

2. Now consider the second figure KLMNP, Sydney's pyramid:

The lateral area is $4* \frac{1}{2}* 4 \sqrt{5} *2x=16 \sqrt{5}x$

so the total area of the second pyramid is $20+16 \sqrt{5}x$

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i) the lateral area of Sydney's pyramid is $\frac{16 \sqrt{5}x}{4\sqrt{5}x} =4$ times larger than the lateral area of the original pyramid.

ii) The total area of Sydney's pyramid is $(20+16 \sqrt{5}x)-(20+4\sqrt{5}x)=12\sqrt{5}x$ units squared larger than the total area of the original pyramid.

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