The diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 meters more than the shorter side, find the length of the field.

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120

187

answer is C.

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Detailed Solution

Concept- Use the Pythagorean theorem

to solve this problem. For simplicity, write the diagonal line and the long side as the short side.
Assume that the diagonal of the rectangular field is 60 meters larger than the short side, and the long side is 30 meters larger than the short side.
The short side is x meters long.
We can write the diagonal on the short side as:

The long side can be written as:

Now let's look at the diagram of the field.
seo

All the angles (vertices) of the rectangle are 90°. Using the right triangle ABC and the Pythagorean theorem,
Question Image

Expanding the above we get:

By factoring the above equation we get:
Question Image

Take the two values of the short side x as 90 or -30. Now we know that the length can never be negative, so the short side value is x = 90 meters.
Substituting the value of x for the length of the long side, we get:

Hence, the correct answer is option is (3) .

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