Q. The diagonal of rectangular field is 60 meters more than the shorter side. If the longer side is 30 m more than the shorter side, find the sides of the field.

Ans:  Let’s consider the shorter side of the field be X m.

Hence, the longer side will be (X + 30) m (by given condition) …… (i)

Also the diagonal of the field will be (X + 60) m (by given condition) …… (ii)

Now, we know that the diagonal of a rectangle is given by:

Therefore, X = 90 and X = -30

Here, we reject X  = – 30 because a side can not be negative value, and we accept X = 90 only

Hence, shorter side, X = 90 m

From Equation (ii), we get longer side = X + 30 = 90 + 30 = 120 m

Hence, sides of the squares are 90 m and 120 m.

Check:

If shorter sides of the filed is 90 m, and the longer side is 120 m, the diagonal of the field will be

Since, this diagonal is 150 – 90 = 60 m longer than the shorter side and it meets 1st given condition, hence our answer is correct.

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