Problem $3\mathrm{.}3$: Consider the gravity dam shown in Figure $3$ Determine the bottom width of this dam such that a triangular base pressure develops at foundation level. Ignore ice, silt, and earthquake forces. Take ${}_c=30$MPa, ${}_1=90$MPa, and $=1\mathrm{.}0.$ Specific weights of water and concrete are $10k\frac{N}{m^3}$ and $24k\frac{N}{m^3},$ respectively.

Figure $3.$ Cross section of the dam