Answer:
Step-by-step explanation:
Given :
In the given quadrilateral ABCD,
BN and DM are the perpendiculars drawn to AC such that,
BN = DM
To prove:
Point O is the midpoint of segment BD.
Or
OD = OB
Solution:
In ΔOMD and ΔONB,
∠MOD ≅ NOB [Vertical angles]
∠M ≅ ∠N ≅ 90° [Given]
Therefore, by AA property of similarity,
ΔOMD ~ Δ ONB
Therefore, their corresponding sides will be proportional,
Since BN = DM,
OD = OB
Hence O is the midpoint of BD.
Answer:
7 pieces
Step-by-step explanation:
Stock that must be available at the beginning of each month = 26 yards
Since,
1 yard = 36 inches
26 yards = 26 x 36 = 936 inches
This means 936 inches of fabric must be available at beginning of each month.
<u>Current Inventory:</u>
4 pieces that are each 22 1/2 (or 22.5) inches long. So total length of these fabrics = 4 x 22.5 = 90 inches
3 pieces that each 33 inches long. So total length of these fabrics = 3 x 33 = 99 inches
Therefore, the total length of current inventory = 90 + 99 = 189 inches.
<u>Length of fabric needed more:</u>
Length of fabric that must be bought more = 936 - 189 = 747 inches
It is given that the fabric must be bought in pieces are the 3 yards long. 3 yards is equal to 108 inches.
So, I have to buy pieces that are each 108 inches long and I need to complete 747 inches in total.
Therefore, the number of pieces that I need to buy =
Since, the pieces cannot be bought in fraction, I need to buy 7 complete pieces to replenish my stock.