The area and perimeter of a square plot of land, whose diagonal length is 15 meters, are sq m and m respectively.

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Detailed Solution

Concept- The area and perimeter of the square plot of land is 112.50 sq m and 42.43 m respectively.
Below shown is a diagram of a square ABCD with a diagonal. Question Image

Here, we can see that diagonal AC forms a right-angled triangle with sides AD and DC, the right-angle being at D. Therefore, in the triangle ADC,
Let us suppose, AD to be the perpendicular, DC to be the base and AC to be the hypotenuse. Since AD and DC are both sides of a square, let us assume their lengths to be

. Then as per the Pythagorean theorem,
“In case of a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides”
Question Image

i.e., According to pythagoras theorem,
Question Image

Here, we will use this relation with AD, DC and AC to form an equation with

and solving for

will give us the length of each side of the square.
Then, we will use the formula of
[Area of a square = (length of a side of the square)2]
and, [Perimeter of a Square = (4× length of a side of the square)]
to obtain our desired answers.
Given, the diagonal of the square is 15 meters, i.e., DC = 15.
Now, using the pythagorean theorem on triangle ADC, we get,
Question Image

Hence, the Correct Answer is 112.50 sq. m. and 42.43 m.

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