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Ivahew [28]
3 years ago
8

Can you help me number 8 and 9

Mathematics
1 answer:
nasty-shy [4]3 years ago
7 0
The area of square ADEF is 32
And the area of triangle ACD is 12.
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Given rectangle ABCD, segment AC is a diagonal, segment BE is perpendicular to segment AC at E. Segment AE = 8 inches and segmen
andriy [413]
Check the picture attached.

Let m(BAE)=m(ACD)=α

(BAE and ACD are congruent, since they are alternate interior angles, or Z angles)

Let m(ABE)=β. 

So in triangle ABE, the measures of the angles are 90, α and β degrees.

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thus, we have the similarity of triangles ABE and BCE,

so the following rations are equal:

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so 

\frac{x}{5} = \frac{8}{x}

x^{2} =40

x= \sqrt{40}= \sqrt{4*10}=2 \sqrt{10}   (inches)


Remark, we can also apply Euclid's theorem directly.

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