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Chapter 11: Q. 90 (page 774)

Geometry: Find formulas for the base b and one of the equal sides l of an isosceles triangle in terms of its altitude h and perimeter P.

Short Answer

Expert verified

We have l=4h2+P24Pandb=P2-4h22P.

Step by step solution

01

Step 1. Given information

For an isosceles triangle,

h=4l2-b22

andP=2l+b.

02

Step 2. Solve the system of equations.

From second equation,

P=2l+bP-2l=bb=P-2l

Substitute this in first equation,

role="math" localid="1646984519275" h=4l2-(P-2l)22h2=4l2-(P2-4Pl+4l2)44h2=4l2-P2+4Pl-4l24h2=4Pl-P24h2+P2=4Pl4h2+P24P=l

03

Step 3. Substitute l=4h2+P24P in b=P-2l.

We get

b=P-4h2+P24P脳2=P-4h2+P22P=P2-4h22P

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Most popular questions from this chapter

In Problems 23鈥�34, graph each system of linear inequalities by hand. Verify your results using a graphing utility

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Verify that the values of the variables listed are solutions of the system of equations.

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