Question

At each corner of a triangular field of sides 26 m, 28 m and 30m, a cow is tethered by a rope of length 7 m. The area (in m2) ungrazed by the cows is

• A. 336
• B. 154
• C. 259
• D. 77

Answer 1

Answer:

C. 259

Rope length r= 7m = radius

Area grazed by all cows $=\frac{\theta}{360^o}\times{\pi{r^2}}$

$=\frac{180^o}{360^o}\pi{r^2}=\frac{\pi{r^2}}{2}$

$=\frac{1}{2}\times{\frac{22}{7}}\times{7}\times{7}=77cm^2$

Semi-perimeter of triangular field $S=\frac{26+28+30}{2}=42metres$

Area of the field $=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{42(42-26)(42-28)(42-30)}$

$=\sqrt{42\times{16}\times{14}\times{12}}$

$=336sq.m$

Area ungrazed by the cows = 336 – 77 = 259 sq.metre