Question

Shamsher has a field in the shape of right angled  triangle with perpendicular sides of length 144m  and 84 m.He wants to leave a space in the form  of a square of largest size inside the field for  growing wheat and the remaining for  growing  vegetables for his family based on the above information answer Q1 to Q4 1. Choose the correct criterio of this ​

Answer 1

To Find :- The length of side of square space.

Solution :-

Let ∆ABC is right angled ∆ with AB as b m and BC as a m and let side of square DEFB is x m .

As we can see that, FC || DE , EF || AD and CE || EA .

So,

→ ΔADE ~ ∆EFC .

then,

→ AD/DE = EF/FC

→ (b - x)/x = x/(a - x)

→ x * x = (a - x)(b - x)

→ x² = ab - x(a + b) + x²

→ x(a + b) = ab

→ x = {ab/(a + b)}

therefore,

→ Side of square = (144 * 84)/(144 + 84) = (144 * 84)/228 ≈ 53.05 m (Ans.)

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