Question

the side of a square is 25 cm find the length of diagonal correct to 2 decimal place

Answer 1

Start from a squareABCD. Now consider thetriangleABC. It's a right triangle, whose catheti are the sides of the square, and whose hypotenuse is the diagonal of the square.Now, Pythagoras' theorem tells us thatoverline(AB)^2 + overline(BC)^2 = overline(AC)^2ButABandBCare both sides of the square, and then they both equal a certain quantityl, whileACis the diagonal and equals10cm. The previous identity becomes2d^2 = 100 \implies d^2 = 50 \implies d=sqrt(50)If you like it, you can simplifysqrt(50)intosqrt(25*2)=sqrt(25)*sqrt(2)=5sqrt(2).I hope this answer is helpful to you

Answer 2

d = √(25^2)+(25^2) = √625+625 = √1250 = 25×1.41 = 35.25

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