Question

Below you see a student's mathematical model of a farmhouse roof with measurements. The attic floor, ABCD in the model, is a square. The beams that support the roof are the edges of a rectangular prism, EFGHKLMN. E is the middle of AT, F is the middle of BT, G is the middle of CT, and H is the middle of DT. All the edges of the pyramid in the model have a length of 12 m.

What is the length of EF, where EF is one of the horizontal edges of the block?
24m
3m
6m
10m​

Answer 1

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Area Of Attic floor ABCD = $\bf{ {144m}^{2} }$

The length of EF =6cm

$\bf{\underline{Explanation-}}$

Area of Attic floor ABCD = AB*BC

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Area of Attic floor ABCD =$\bf{ {144m}^{2} }$

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E is the middle of AT ⇒ ET ⇒AT/2 = 6 cm

F is the middle of BT ⇒FT ⇒ BT/2 = 6 cm

ΔTEF = ΔTAB

⇒ET/AT = FT/BT = EF/AB

$⇒ \frac{6}{12} = \frac{6}{12} = \frac{EF}{12}$

$\bf{\underline{EF = 6cm}}$

${\underline{\boxed{{\sf{The \: length \: of \: EF \: = 6 \: cm}}}}}$

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Answer 2

Direct Answer :

➻ Area of the attic floor = 144m²

➻ Length of EF = 6m

Explanation :

Area of the attic floor ABCD = AB × BC

: ⟼ (12 × 12) m

: ⟼ 144m²

Area of the attic floor ABCD = 144m².

✇ E is the middle of AT.

: ⟼ ET = AT/2

: ⟼ ET = (12/2)m ㅤㅤㅤㅤㅤㅤㅤ[AT = 12m]

: ⟼ ET = 6m

✇ F is the middle of BT.

: ⟼ FT = BT/2

: ⟼ FT = (12/2m) ㅤㅤㅤㅤㅤㅤㅤ[BT = 12m]

: ⟼ FT = 6m

➻ ∆TEF ≈ ∆TAB

⟹ ET/AT = FT/BT = EF/AB

⟹ 6/12 = 6/12 = EF/12

⟹ EF = 6m

The length of EF = 6m.

Therefore :

Option C (6m) is the correct option.

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