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Chapter 6: Q53. (page 292)

WRITING IN MATH

A rectangle is inscribed in an isosceles triangle as shown. Find the dimensions of the inscribed rectangle with maximum area. (Hint: Use similar triangles.)

Short Answer

Expert verified

Thedimensions are 5脳4inches

Step by step solution

01

Step 1. Given information

A figure is given as above

02

Step 2. Concept used

Make a quadratic equation by assuming one side as $x$. Find the maximum value of it and then find the value of dimensions.

03

Step 3. Calculation

Let x=the length of the rectangle.

Then 8-45x=the height of the rectangle.

=x(8)+x鈭�45x=8x鈭�45x2=鈭�45x2+8x

A(x)is a quadratic function with a=-45,b=8, and c=0. Since a<0, the function has a maximum value at the vertex of the graph.

=鈭�82鈭�45=5

This means the maximum area occurs with length 5 inches and height 8-45(5) or 4 inches.

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Most popular questions from this chapter

Complete parts a-c for each quadratic function.

  1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
  2. Make a table of values that includes the vertex.
  3. Use this information to graph the function.

f(x)=3x2+1

Simplify

7+2i1-i

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

-x2+x=-20

Find the coordinates of the maximum or minimum value of each quadratic equation to the nearest hundredth.

fx=7x2+4x+1

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

-x2+4x=0
See all solutions

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