Solve the problem.
-The figure shown here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 10 units long. Express the area A of the rectangle in terms of x.
A) $A(x)=2 x^{2}$
B) $A(x)=2 x(x-5)$
C) $A(x)=x(5-x)$
D) $A(x)=2 x(5-x)$

Question

Solve the problem.
-The figure shown here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 10 units long. Express the area A of the rectangle in terms of x. 
A) $A(x)=2 x^{2}$ 
B) $A(x)=2 x(x-5)$ 
C) $A(x)=x(5-x)$ 
D) $A(x)=2 x(5-x)$

Quizplus · Accepted Answer

Let the legs of the isosceles right triangle be $x$ each. Then the hypotenuse is $10$, so $x\sqrt{2}=10\Rightarrow x=5\sqrt{2}$. The dimensions of the rectangle are $x$ and $5-x$, so $A(x)=x(5-x)=5x- x^2= 2x(5-x)$. Therefore, the correct answer is $\boxed{	extbf{(D)}}$.

Solve the Problem A(x)=2x2A(x)=2 x^{2}A(x)=2x2 B) A(x)=2x(x−5)A(x)=2 x(x-5)A(x)=2x(x−5) C) A(x)=x(5−x)A(x)=x(5-x)A(x)=x(5−x) D) A(x)=2x(5−x)A(x)=2 x(5-x)A(x)=2x(5−x)

Solve the Problem $A(x)=2 x^{2}$ B) $A(x)=2 x(x-5)$ C) $A(x)=x(5-x)$ D) $A(x)=2 x(5-x)$