The sides of a parallelogram are 10 and 11. The integral value of the

Question

The sides of a parallelogram are 10 and 11. The integral value of the length of the diagonal opposite to the acute angle is at most

A. 13
B. 14
C. 15
D. 19
E. 20

Lipun · Answer

Maximum length of the diagonal will occur when the acute angle is close to 90

=> Maximum length of the diagonal will be the integer value less than the diagonal value if it were a right angle.

=> Maximum length =   =   = 14

- denotes the lower integral value.

Ans: B

yashikaaggarwal · Answer

Let the triangle be a right angle triangle.
Therefore,
Side1^2 + Side2^2 = Diagonal^2
10^2 + 11^2 = Diagonal^2
100+121 = Diagonal^2
221 = Diagonal^2
Diagonal = 14.86 (approx)

Since diagonal is of the acute angle. It has to be least than 14.86
The maximum integral value of the diagonal less than 14.86 is 14

Answer is B

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AabhishekGrover · Answer

how to calculate 14.86 from root(221)

maggiesomi · Answer

i don't even understand what the question is asking...
can anyone draw a graph please? Thank you.

maggiesomi · Answer

well, i guess since 15^2= 225 and 14^2 = 196, \sqrt{221} must between 14 and 15.

Lipun · Answer

Refer attached figures. In fig 1, angle ABC is obtuse and angle BCD is acute. We are asked to find the length of diagonal opposite to the acute angle. => Length of BD. Now we need to understand how are the diagonals related to the angle opposite to them. Fig 2 is a rectangle. => BD^2 = BC^2 + CD^2 If the angle increases to more than 90 degrees, then the length of diagonal BD will increase. Thus, BD^2 will no longer be equal to BC^2 + CD^2. BD^2 > BC^2 + CD^2. This is true of diagonal AC in figure 1. AC^2 > AB^2 + BC^2 If the angle decreases to less than 90 degrees, then the length of diagonal BD will decrease. Thus, BD^2 < BC^2 + CD^2 in figure 1. We need to find the maximum possible integral value of BD when the angle is acute. This will happen when the angle is almost but less than 90. So, the length of BD will be slightly less than what it would be if the angle were a right angle. BD^2 < BC^2 + CD^2 => BD^2 < 11^2 + 10^2 => BC^2 < 121 + 100 => BC^2 < 221 We don't need to calculate the exact value of BD. We simply need to know the range of squares that it lies between. => 196 < BD^2 < 225 => 14^2 < BD^2 < 15^2 => The maximum integral value of BD (diagonal opposite the acute angle) will be 14. Hope it helps!

kawal27 · Answer

for approximate value we can consider diagonals bisects each other at 90
so 10^2=8^2+6^2 
 
 so diagonal = 8+6=14 approx 
 ANS:B

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The sides of a parallelogram are 10 and 11. The integral value of the

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The sides of a parallelogram are 10 and 11. The integral value of the

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