If the projections of the legs onto the hypotenuse in a right triangle are, respectively, 6cm and 12cm, then the triangle's area is equal to: (A) 18cm^(2) (B) 18sqrt(2)cm^(2) (C) 36sqrt()3cm^(2) (D) 18sqrt3cm^(2) (E) 54sqrt()2cm^(2)

Denote legs and hypotenuse: Let's denote the legs of the right triangle as a and b, and the hypotenuse as c. The projections of the legs onto the hypotenuse are given as 6 cm and 12 cm. According to the properties of right triangles, the product of the projections is equal to the area of the triangle. So, the area (A) can be calculated as: A = (projection of a onto c) * (projection of b onto c) A = 6 cm * 12 cm A = 72 cm^2

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Q. If the projections of the legs onto the hypotenuse in a right triangle are, respectively,

6 \mathrm{~cm}

and

12 \mathrm{~cm}

, then the triangle's area is equal to:

\newline

(A)

18 \mathrm{~cm}^{2}

\newline

(B)

18 \sqrt{ } 2 \mathrm{~cm}^{2}

\newline

(C)

36 \sqrt{ } 3 \mathrm{~cm}^{2}

\newline

(D)

18 \sqrt{3} \mathrm{~cm}^{2}

\newline

(E)

54 \sqrt{ } 2 \mathrm{~cm}^{2}

Denote legs and hypotenuse: Let's denote the legs of the right triangle as $a$ and $b$ , and the hypotenuse as $c$ . The projections of the legs onto the hypotenuse are given as $6$ cm and $12$ cm. According to the properties of right triangles, the product of the projections is equal to the area of the triangle. So, the area ( $A$ ) can be calculated as: $\newline$ $A = (\text{projection of } a \text{ onto } c) \times (\text{projection of } b \text{ onto } c)$ $\newline$ $A = 6 \text{ cm} \times 12 \text{ cm}$ $\newline$ $A = 72 \text{ cm}^2$