Solve for unknown measures

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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 6 2 = 12 inches. ANSWER

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.

(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

Solve a multi-step problem EXAMPLE 3 Solve a multi-step problem STEP 3 Determine how many gallons of paint you need. 637 ft2  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.

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. ANSWER 9 in.

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. ANSWER 587 ft2