Question

the perimeter of a rectangle is 50m and area is 300 square m.Diagonal of rectangle is equal to diagonal of square then find area of square.​

Answer 1

Answer:

Step-by-step explanation:

perimeter = 2(a+b)

where a and b are the sides of the rectangle

a+b = perimeter / 2 = 25

squaring

$a^{2} + b^{2} + 2ab$ = 25 x 25 ----------------1

now

$a^{2} + b^{2} = diagonal^{2}$

and

ab = area = 300

putting the values in equation 1

we get

diagonal^2 + 2(300) = 625

diagonal^2 = 25

diagonal = 5

also

diagonal of a square = s$\sqrt{2}$ where s is one of the 4 equal sides

therefore

5 = s$\sqrt{2}$

s = 5/$\sqrt{2}$

multiplying and dividing by $\sqrt{2}$  we get

s = 5$\sqrt{2}$ /2

s = 2.5$\sqrt{2}$ hope it helps

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