A carpenter is framing an opening in a wall to hang a rectangular door. Which properties must the door frame have to ensure that
2 answers:
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Answer:
46 cm
Step-by-step explanation:
It is given that the angle bisector AC divides the trapezoid ABCD into two similar triangles Δ ABC and Δ ACD.
Let us first find the corresponding sides of triangles Δ ABC and Δ ACD.
Since AC is the angle bisector of ∠A,
∠DAC = ∠CAB --- (1)
Also, since ∠DAC and ∠ACB are alternate interior angles,
∠DAC = ∠ACB --- (2)
From (1) and (2),
∠CAB = ∠ACB
Therefore, in Δ ABC,
BC = AB (sides opposite to equal angles are equal)
So, BC = 9 cm.
Now, since ∠DAC = ∠ACB and ∠DAC = ∠CAB, we can take either ∠ACB or ∠CAB as the angle corresponding to ∠DAC. Let us take ∠ACB as the corresponding angle of ∠DAC.
So, the side opposite to ∠DAC in Δ ACD is the corresponding side to the side opposite to ∠ACB in Δ ABC.
That is, the side CD in Δ ACD is the corresponding side to the side AB in Δ ABC.
Now, suppose if the side BC in Δ ABC corresponds to side AD of Δ ACD, then the remaining side AC of Δ ABC should correspond to side AC of Δ ACD which is not possible since they are congruent.
So, the side BC in Δ ABC should correspond to side AC of Δ ACD and the remaining side AC of Δ ABC should correspond to side AD of Δ ACD.
Therefore, we have,
But,
Therefore,
AC = 12 cm
Also,
AD = 16 cm
Now, the perimeter of the trapezoid = AB + BC + CD + AD
= 9 + 9 + 12 + 16
= 46 cm
Answer:
so the closet value will be 21.
Step-by-step explanation:
In this question we have to calculate the value of 85% of 25.
To calculate the percentage first we have to write percentage to the fraction and then multiply with 25.
× 25
= 0.85 × 25
= 21.25
Therefore, the closet value of 21.25 will be 21 because when we round off, 0.25 will be waved off. Had this value been greater than 0.50 or equal to 0.5 than this value would have been 22.
so the closet value will be 21.