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Chapter 2: Q. 90 (page 70)

Geometry Express the area A of an isosceles right triangle as a function of the length x of one of the two equal sides.

Short Answer

Expert verified

The area of isosceles right triangle isA(x)=12x2

Step by step solution

01

Step 1. Given Information

Express the area A of an isosceles right triangle as a function of the length x of one of the two equal sides.

02

Step 2. We know that the area of isosceles triangle A=12×base×height

The length of one of the two equal sides is x.

The value of base=xand height=x

03

Step 3. Putting the value in the formula

A(x)=12×x×x

The area of isosceles right triangle

A(x)=12x2

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Most popular questions from this chapter

In Problems 7–18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

Exploration Graph y=x. Then on the same screen graph y=-x. What pattern do you observe? Now try y=2x+1 and y=2(-x)+1. What do you conclude?

A wire 10meters long is to be cut into two pieces. One piece will be shaped as an equilateral triangle, and the other piece will be shaped as a circle.

Part (a): Express the total area Aenclosed by the pieces of wire as a function of the length x of a side of the equilateral triangle.

Part (b): What is the domain of A?

Part (c): Graph A=Ax. For what value of xis Asmallest?

In Problems 7–18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

A semicircle of radius r is inscribed in a rectangle so that the diameter of the semicircle is the length of the rectangle. See the figure.

(a) Express the area A of the rectangle as a function of the radius r of the semicircle.

(b) Express the perimeter p of the rectangle as a function of r.
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