Question

The length of a field is 40 m and breadth 30 m, then what will be the diagonal of that field?​

Answer 1

Answer:

Length = 30 m.

Breadth = 40 m.

Diagonal can be found by dividing the rectangle along the diagonal.

This forms 2 congruent right angle triangles.

According to Pythagorean theorem:

In a right angle triangle, hypotenuse² = adjacent side² + opposite side².

Here:

diagonal is the hypotenuse.

length is the adjacent side.

breadth is the opposite side.

Let the diagonal be denoted by the variable x.

So,

x²=30²+40².

x²=900+1600.

x²=2500.

x=√2500.

x=50.

Therefore, the length of the diagonal is 50 m.

When the person walks using the length and breadth of the rectangle he covers 30+40 = 70 m, but when he walks using the diagonal of the rectangle he covers 50 m only.

So, he saves 70-50 = 20 m by walking diagonally across it.

Hence, the person saves 20 meters by walking diagonally across.

Answer 2

• As per the data given in the question, we have to determine the diagonal of the rectangular field.

        Given data:- Length=$40m.$

                             Breadth=$30m.$

         To find:- the diagonal of field.

          Solution:-

• We will know that,

        $\Rightarrow h^{2}=\sqrt{l^{2}+b^{2} }}\\\Rightarrow h^{2}=\sqrt{40^{2}+30^{2} }}\\\Rightarrow h^{2}=\sqrt{1600+900}\\\Rightarrow h^{2}=\sqrt{2500}\\ h=50m.$

    Hence, the diagonal of field is $50m.$