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Challenge 236: Magnificent Maximising

a        A triangle ABC is right angled at B and has base AB of length 24 and height BC of length 6.

A rectangle is drawn with sides parallel to AB and BC, and with one vertex at B, one at P on AB, one at Q on AC and one at R on BC. The height of this rectangle is a.

Find the value of a which makes the area of the rectangle as large as possible.

 

b       A triangle ABC is right angled at B and has base AB of length 24 and height BC of length 6.

A rectangle is drawn with sides parallel to AB and BC, and with one vertex at B, one at P on AB, one at Q on AC and one at R on BC. The height of this rectangle is a.

A second rectangle is drawn with sides parallel to AB and BC, and with one vertex at R, one at S on QR, one at T on AC and one at U on BC, one at P on AB, one at Q on AC and one at R on BC. This rectangle has height b.

Find the values of a and b which make the combined area of the two rectangles as large as possible.

 

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