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3 years ago

6

Jarred has two cakes that are the same size.The first cake was chocolate,which he cut 12 equal parts.The second cake was marble,

which he cut into 6 equal parts.His family eats 5 slices of chocolate cake and 3 slices of marble cake.

1 answer:

Readme [11.4K]3 years ago

4 0

Whats the question? There is 7 pieces of chocolate and 3 pieces of marble left...

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What is the length of AC?<br><br><br> 3 ft<br><br> 4 ft<br><br> 9 ft<br><br> 18 ft

iragen [17]

Answer: The length of AC is 18 ft.

Step-by-step explanation:

By the given diagram,

AM = MB and CN = NB

M and N are the mid points of the sides AB and CB respectively,

Thus, by the mid point theorem,

MN ║ AC,

By the alternative interior angle theorem,

∠BMN ≅ ∠BAC

∠BNM ≅ ∠BCA

Thus, by AA similarity postulate,

ΔBMN ≅ ΔBAC

By the property of similar triangles,

$\frac{BM}{BA}=\frac{MN}{AC}$

$\frac{BM}{BM+MA}=\frac{MN}{AC}$

$\frac{4}{4+4}=\frac{9}{AC}$

$\frac{4}{8}=\frac{9}{AC}$

$4AC=72\implies AC = 18\text{ ft}$

Thus, The length of AC is 18 ft.

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