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Chapter 11: Q. 351 (page 1161)

For her birthday, Olive鈥檚 grandparents bought her a new widescreen TV. Before opening it she wants to make sure it will fit her entertainment center. The TV is 55鈥�. The size of a TV is measured on the diagonal of the screen and a widescreen has a length that is larger than the width. The screen also has an area of 1452

square inches. Her entertainment center has an insert for the TV with a length of 50 inches and width of 40 inches. What are the length and width of the TV screen and will it fit Olive鈥檚 entertainment center?

Short Answer

Expert verified

The solution is circle and hyperbola.

Step by step solution

01

Step 1. Given Information

The TV is 55inches. The area of the screen is 1452square inches.

02

Step 2. Standard form of equation

The equation can be obtained as,

x2+y2=3025xy=1452

The equation can be expressed as,

role="math" localid="1645335101281" (x-0)2+(y-0)2=3025(h,k)=(0,0),r=55xy=1425x=1425x

The standard form ofx2+y2=3025is(x-0)2+(y-0)2=552andxy=1452isx=1452x.

03

Step 3. Substitution method

Let's take length and width of the rectangle are x and y.

x2+y2=30251452x2+y2=3025y2-1936=0y=44,y=33x=33,x=44

04

Step 4. Graph of the equation

The graph of the equation can be drawn as,

The point of intersection is (33,44) and (-44,-33).

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