find the ratio of the area of the triangle ACD to the area of the triangle ABE

bumblebee123

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Jan 3, 2018
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Does anyone know how to answer these questions?

question:
a)
find the ratio of the area of the triangle ACD to the area of the triangle ABE

b) find the ratio of the ara of the triangle ABE to the are of the trapezium BCDE

11813
any help would be really appreciated :)
 
a) Hint: The area of any plane figure is proportional to the square of any of its linear measures. For similar shapes, and corresponding linear measures, the constant of proportionality is the same.

Can you now find the requested ratio?
 
a) Hint: The area of any plane figure is proportional to the square of any of its linear measures. For similar shapes, and corresponding linear measures, the constant of proportionality is the same.

Can you now find the requested ratio?

so 5^2 : 4^2
25 : 16

thanks this is correct!

I'm still not sure about b) though
 
Let's let the area of \(\triangle ACD\) be 1 unit. From part a) we can then say the area of \(\triangle ABE\) is [MATH]\frac{16}{25}[/MATH]. So, then what must be the area of trapezium \(BCDE\)?
 
Let's let the area of \(\triangle ACD\) be 1 unit. From part a) we can then say the area of \(\triangle ABE\) is [MATH]\frac{16}{25}[/MATH]. So, then what must be the area of trapezium \(BCDE\)?

25 - 16 = 9 so

area of trapezium BCDE = 9/ 25

therefore the ratio if ABE to BCDE = 16: 9

thanks, this makes sense!
 
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