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Nata [24]
3 years ago
15

The base of a triangle is twice the height of the triangle.

Mathematics
1 answer:
Andreas93 [3]3 years ago
6 0

Answer:

<h3>4cm</h3>

Step-by-step explanation:

area =  \frac{1}{2} \times base \times height \\ 16 {cm}^{2}  =  \frac{1}{2}  \times 2x \times x \\ 16 {cm}^{2}   =  \frac{2 {x}^{2} }{2}  \\ \\ 16 {cm}^{2}  \times 2 = 2 {x}^{2} \\ 32 {cm}^{2}  = 2 {x}^{2}  \\  \frac{32 {cm}^{2} }{2}  =  {x}^{2}  \\ 16 {cm}^{2}  =  {x}^{2}  \\  \sqrt{16 {cm}^{2} }  =  \sqrt{ {x}^{2} }  \\ 4cm = x \\

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Step-by-step explanation:

The picture of the question in the attached figure

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A(x)=-x^2+240x

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A(x)=-x^2+240x

Factor -1

A(x)=-(x^2-240x)

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A(x)=-(x^2-240x+120^2)+120^2

A(x)=-(x^2-240x+14,400)+14,400

A(x)=-(x-120)^2+14,400

The vertex is the point (120,14,400)

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The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

x=120\ m

W=(240-120)=120\ m

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A=120^2=14,400\ m^2

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