Using Algebra To Solve Geo Problems

Chapter

10 - The Basics

of Algebra

I 311

Using Algebra to Solve Geometry Problems Study the next examples carefully to see how to substitute algebraic expressions into geometry formulas. Example 'I

The perimeter of a rectangle is 74 inches. The I ngth of the rectangle is 5 inches more than the width. Find the length of the rectangle.

Step 1

Let x represent the width and x + 5 the length.

width = x length = x + 5

Step 2

Substitute 74 for P, x + 5 for the Ie gth, and x for the width in the formula for the perimeter of a rectangle.

P = 21 + 2w 74 = 2(x + 5)

+ 2x

74 = 2x + 10 + 2x 74 = 4x + 10 64 = 4x 16 = x Step 4

Example 2

Step.1

Substitute 16 for x in he expression x + 5 to find the length. he length is 21 inches.

length = x + 5 = 16 + 5 = 21

In the iIIustratiorn at the right, LADe is a right angle. What is the measure of~ADB?

Write an equation that shows the sum of the angles equal 90°. 5x = 90 x = 18

Step 3

Substitute 18 for x in the expression for LADB. 4x = 4(18) = 72° The measure of LADB is 72°.

318 I

Mathematics

Directions:

Solve each problem.

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1. Find the measure, in degrees, of the smallest angle iF}the triangle pictured at the right.

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2. A rectangle has a perimeter of 48 feet. The length is t~~' , .e width. Find the measure of 1he width of the rectangle. Y: j() ;:::LfQ f 3. In the illustra-k6n a{the righPLAOC I A measures 90°. Find the measure of

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4. A rectangle has a perimeter of 60 inches. The ratio of the width to

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ofthe rectangle in inches.

5. Fin"dthe mea~~e o~AOl5'in"'" the illustration at the rig~

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For the rectangle at the right, the ratio of WXto WZ is 5:6. The perim of the rectangle is 110 feet. Find the length of WZ in feet.

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Find the measure of LAOD in the illustration at the right.

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Chapter

8.

10 - The Basics of Algebra

Ql

The perimeter of the rectangle pictured at the right is 34 feet. MP is 3 feet longer than MN. Find the measure fl'N in feet.

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I 319

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9.

How many degrees are there in LW in the illustration at the right?

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[5]

The perimeter ofthe square pictured at the right is equal to the perimeter of the rectangle. Solve for x.

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)~-tr-) Answers are on page 431.

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