Answer for the 3 sums

Answer for the 3 sums • the centroid ABC. AD = 8, AG = 10, BE — the length of each segmenV. length of Felix's room is corners is 20 feet. What f-z . lithe square ofthe , each side.

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$$\begin{gathered} \mathbf{Q}\mathbf{3}. \mathrm{Given} \mathrm{length} \mathrm{of} \mathrm{square} \mathrm{of} \mathrm{hypotenuse} \mathrm{of} \mathrm{an} \mathrm{isosceles} \mathrm{right} \mathrm{triangle} = 128 {\mathrm{cm}}^2 \\ \mathrm{In} \mathrm{an} \mathrm{isosceles} \mathrm{triangle} \mathrm{two} \mathrm{sides} \mathrm{have} \mathrm{same} \mathrm{length}. \mathrm{Let} \mathrm{the} \mathrm{equal} \mathrm{sides} \mathrm{be} \text{'}\mathrm{a}\text{'} \mathrm{cm} \\ \mathrm{By} \mathrm{pythagoras} \mathrm{theorem}, \mathrm{we} \mathrm{have} \\ {\mathrm{AC}}^2 = {\mathrm{a}}^2+{\mathrm{a}}^2= 2{\mathrm{a}}^2 \\ 2{\mathrm{a}}^2 = 128 \\ {\mathrm{a}}^2 = \frac{128}{2} = 64 \\ \mathrm{a} = \sqrt{64} = 8 \mathrm{cm} \\ \mathrm{Hence}, \mathrm{the} \mathrm{length} \mathrm{of} \mathrm{equal} \mathrm{sides} \mathrm{is} 8 \mathrm{cm} \end{gathered}$$

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