Question

Solve and answer this question.

Answer 1

For a rectangle;

$length \: (l) = \frac{1}{3} {x}^{2} + \frac{1}{2} \\ \\ perimeter = \frac{2}{3} {x}^{2} + \frac{13}{4} \\ 2(l + b) = \frac{2}{3} {x}^{2} + \frac{13}{4} \\ 2l + 2b = \frac{2}{3} {x}^{2} + \frac{13}{4} \\ 2b = \frac{2}{3} {x}^{2} + \frac{13}{4} - 2l \\ 2b = \frac{2}{3} {x}^{2} + \frac{13}{4} - 2( \frac{1}{3} {x}^{2} + \frac{1}{2} ) \\ 2b = \frac{2}{3} {x}^{2} + \frac{13}{4} - \frac{2}{3} {x}^{2} - 1 \\ \\ multiplying \: throughout \: by \: 12 \\ \\ 24b = 8 {x}^{2} + 39 - 8 {x}^{2} - 12 \\ 24b = 27 \\ b = \frac{27}{24} \\ b = \frac{9}{8} \: \: \: units$

Hence, measure of the breadth of the given rectangle is 9/8 units.

Answer 2

Answer: 9/8

Explanation is attached below