29.2/10.4 and 7.3/2.3 equivalent ratios
1 answer:
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A tank with capacity T gallons is empty. Tank will be filled in minutes
<u>Solution:</u>
Given, A tank with capacity T gallons is empty.
We have to find how many minutes will tank be filled?
Now, Water flows into the tank from pipe X at the rate of X gallons per minute,
And water is pumped out by pipe Y at the rate Y gallons per minute,
Then, together in one minute the amount of water filled will be x – y gallons [as X is greater than Y]
Now, the time take to fill tank =
Hence tank will be filled in minutes
Angles formed by the segment in the triangles ΔWXZ, and ΔXYZ, are equal and the given corresponding sides are proportional.
- The option that best completes the proof showing that ΔWXZ ~ ΔXYZ is; <u>16 over 12 equals 12 over 9</u>
Reasons:
The proof showing that ΔWXZ ~ ΔXYZ is presented as follows;
Segment is perpendicular to segment
∠WZX and ∠XZY are right angles by definition of perpendicular to
∠WZX in ΔWXZ = ∠XZY in ΔXYZ = 90° (definition)
Therefore;
, which gives,
Given that two sides of ΔWXZ are proportional to two sides of ΔXYZ, and
that the included angles between the two sides, ∠WZX and ∠XZY are
congruent, the two triangles, ΔWXZ and ΔXYZ are similar by Side-Angle-
Side, SAS, similarity postulate.
The option that best completes the proof is therefore;
Learn more about the SAS similarity postulate here: