3.4(ii) Real life problems based on variation

Example 1:

The strength "s" of a rectangular beam varies directly as the breadth $b$ and the square of the depth $d$ . If a beam $9\mathrm{c}\mathrm{m}$$9\mathrm{cm}$ wide and $12\mathrm{c}\mathrm{m}$$12\mathrm{cm}$ deep will support $1200\mathrm{l}\mathrm{b}$$1200\mathrm{lb}$ . What weight a beam of $12\mathrm{c}\mathrm{m}$$12\mathrm{cm}$ wide and $9\mathrm{c}\mathrm{m}$$9\mathrm{cm}$ deep will support?

Solution: By the joint variation, we have $s \propto b d^{2}$

Put in eq. (i) $s=\frac{25}{27}b{d}^2$$s = \frac{25}{27} b d^{2}$

Now for $b = 12$ and $d = 9$