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Kirti Agarwal
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I am not able to do this question please help me. Ques 3
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July 5, 2017 at 6:39am
Little Sky
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The answer is [ieqn]825\text{cm}^2[/ieqn] First line is selected randomly with AB as base and followed by random second line with a midpoint as M. Together, base AB and vertex M forms a triangle. Area of triangle => 1/2 * base * height Base is the same for all triangle possibilities which is 5 cm. Only the height varies for all possibilities, with minimum 1 cm and maximum 9 cm. Let the left most line be the 1st line and the right most line be the last line (10th line) Choosing the first line as base, we can choose the 2nd line and its midpoint as vertex to form a triangle, we can also choose 3rd line, 4th line, ..., until 10th line. So, we have 9 combinations of triangle. You can use the formula of area of triangle above to compute the area of triangle. Total area for 1st line as base = 1/2 * 5 * 1 + 1/2 * 5 * 2 + 1/2 * 5 * 3 + ... + 1/2 * 5 * 9 = 1/2 * 5 * ( 1 + ... + 9) Similarly, if we choose the last line (10th line) as a base, we can choose 9th line as vertex, followed by 8th line, 7th line, ... , until 1st line. You will notice that it is just a reflection. Total area for 10th line as base = 1/2 * 5 * 1 + 1/2 * 5 * 2 + 1/2 * 5 * 3 + ... + 1/2 * 5 * 9 = 1/2 * 5 * ( 1 + ... + 9) Total area for 1st and 10th lines as base = (1/2 * 5 * 1 + 1/2 * 5 * 2 + 1/2 * 5 * 3 + ... + 1/2 * 5 * 9) * 2 = 1/2 * 5 * ( 1 + ... + 9) * 2 = 5 * ( 1 + ... + 9) we can carry on with 2nd and 9th line, if you understood the above, you should get Total area for 2nd and 9th lines as base = (1/2 * 5 * 1 + 1/2 * 5 * 1 + 1/2 * 5 * 2 + ... + 1/2 * 5 * 8) * 2 = 1/2 * 5 * ( 1 + 1 + 2 + ... + 8) * 2 = 5 * ( 1 + 1 + 2 + ... + 8) Similarly, Total area for 3rd and 8th lines as base = (1/2 * 5 * 1 + 1/2 * 5 * 1 + 1/2 * 5 * 2 + 1/2 * 5 * 2 + 1/2 * 5 * 3 + ... + 1/2 * 5 * 7) * 2 = 1/2 * 5 * ( 1 + 1 + 2 + 2 + 3 + ... + 7) * 2 = 5 * ( 1 + 1 + 2 + 2 + 3 + ... + 7) You should carry on with 4th & 7th and lastly, 5th and 6th. Total area for 4th and 7th, = 5 * (1 + 1 + 2 + 2 + 3 + 3 + 4 + 5 + 6) Total area for 5th and 6th, = 5 * (1 + 1 + 2 + 2 + 3 + 3 + 4 + 4 + 5) Summing up total area for all of the above, you should get the answer.
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July 6, 2017 at 1:50pm
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