Question

d) kamala wanted to fence the wire distance on that land. if she asks you whether 250 meter 250 metre is enough or not, write your answer with reasons.

Explanation:

Step1: Identify the shape (trapezoid)

The land appears to be a trapezoid with parallel sides \(a = 28\,\text{m}\), \(b = 100\,\text{m}\), height \(h = 35\,\text{m}\), and we need to find the perimeter (fencing length). Wait, actually, the non - parallel side (the slant side) can be found using the Pythagorean theorem. The difference in the parallel sides is \(100 - 28=72\,\text{m}\). So the slant side \(c=\sqrt{35^{2}+72^{2}}\) (since the horizontal difference is \(72\) and vertical is \(35\)).

Step2: Calculate the slant side

First, calculate \(35^{2}=1225\) and \(72^{2} = 5184\). Then \(35^{2}+72^{2}=1225 + 5184=6409\). \(\sqrt{6409}\approx80\,\text{m}\) (since \(80^{2}=6400\), close to \(6409\)).

Step3: Calculate the perimeter

Perimeter \(P=a + b+h + c=28 + 100+35 + 80\). \(28+100 = 128\), \(128+35 = 163\), \(163+80 = 243\,\text{m}\).

Step4: Compare with 250 m

Since \(243\lt250\), the 250 - meter fence is enough.

Answer:

250 meters of fence is enough. The perimeter of the trapezoidal land (calculated as the sum of its four sides, with the slant side found via Pythagorean theorem) is approximately 243 meters, which is less than 250 meters.