The length of the diagonal of a rectangle is √181 inches. Which statement describes the length of the diagonal?
1 answer:
Answer:
The correct option is (B).
Step-by-step explanation:
The length of the diagonal of a rectangle is inches.
Compute the value of inches as follows:
The number 181 is not a square of a whole number.
So, the square root of 181 must lie between two whole numbers.
Consider the following squares:
It is quite clear that the 181 lies between the square of 13 and 14.
So, it can be said that the square root of 181 is between the square of 13 and 14.
Thus, the length of the diagonal of a rectangle is between 13 and 14 inches.
The correct option is (B).
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<span>In triangle WXZ,
Line WY is an altitude (as shown in the attached picture)
Now, it is given that:
</span><span>If ΔYWZ ~ ΔYXW
</span>∠WXY = ∠WZY
<span>
Then, we can also conclude
</span>∠WYX = ∠WYZ = 90°....(1) (because WY is the altitude)
Now, in any triangle, the sum of all the three angles is 180.
In triangle, WXY, ∠WYX = 90° (From 1)
Therefore, WXY + XWY = 90°
Similarly, in WZY.
Hence, we conclude that XWZ is a right angle.
Line WY is an altitude (as shown in the attached picture)
Now, it is given that:
</span><span>If ΔYWZ ~ ΔYXW
</span>∠WXY = ∠WZY
<span>
Then, we can also conclude
</span>∠WYX = ∠WYZ = 90°....(1) (because WY is the altitude)
Now, in any triangle, the sum of all the three angles is 180.
In triangle, WXY, ∠WYX = 90° (From 1)
Therefore, WXY + XWY = 90°
Similarly, in WZY.
Hence, we conclude that XWZ is a right angle.