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**Solve for unknown measures**

EXAMPLE 2 Solve for unknown measures Algebra The base of a triangle is twice its height. The area of the triangle is 36 square inches. Find the base and height. Let h represent the height of the triangle. Then the base is 2h. A = bh 2 1 Write formula. 36 = (2h)(h) 2 1 Substitute 36 for A and 2h for b. 36 = h2 Simplify. 6 = h Find positive square root of each side. The height of the triangle is 6 inches, and the base is = 12 inches. ANSWER

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EXAMPLE 3 Solve a multi-step problem Painting You need to buy paint so that you can paint the side of a barn. A gallon of paint covers 350 square feet. How many gallons should you buy? SOLUTION You can use a right triangle and a rectangle to approximate the area of the side of the barn.

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**(338 ) EXAMPLE 3 Solve a multi-step problem STEP 1**

Find the length x of each leg of the triangle. 262 = x2 + x2 Use Pythagorean Theorem. 676 = 2x2 Simplify. 338 = x Solve for the positive value of x. STEP 2 Find the approximate area of the side of the barn. Area = Area of rectangle + Area of triangle = 26(18) + 1 2 (338 ) = 637 ft2

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**Solve a multi-step problem**

EXAMPLE 3 Solve a multi-step problem STEP 3 Determine how many gallons of paint you need. 637 ft 1.82 gal 350 ft2 1 gal Use unit analysis. Round up so you will have enough paint. You need to buy 2 gallons of paint.

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**Let the length of the base be x**

GUIDED PRACTICE for Examples 2 and 3 A parallelogram has an area of 153 square inches and a height of 17 inches. What is the length of the base? 4. SOLUTION Let the length of the base be x A = b h Write formula. 153 = x 17 Substitute 153 for A and 17 for h and x for b. x = 9 Simplify. ANSWER Length of the base is 9 in.

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**Find the length x of each leg of the triangle.**

GUIDED PRACTICE for Examples 2 and 3 WHAT IF? In Example 3, suppose there is a 5 foot by 10 foot rectangular window on the side of the barn. What is the approximate area you need to paint? 5. SOLUTION You can use a right triangle and a rectangle to approximate the area of the side of the barn. STEP 1 Find the length x of each leg of the triangle. 262 = x2 + x2 Use Pythagorean Theorem. 676 = 2x2 Simplify. 338 = x Solve for the positive value of x.

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**(338 ) GUIDED PRACTICE for Examples 2 and 3 STEP 2**

Find the approximate area of the side of the barn. Area = Area of rectangle + Area of triangle 2 (338 ) = 26(18) + 1 = 637 ft2 STEP 3 Find the area of window. A = l b Write formula. = Substitute. = 50 ft2 Multiply.

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GUIDED PRACTICE for Examples 2 and 3 Find the approximate area you need to paint. STEP 4 Area of side of barn – Area of window = 637 – 50 = 587 ANSWER You need to paint an approximate area of 587 ft2.

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