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EXAMPLE 2

Algebra The base of a triangle is twice its height. The area of the triangle is 36 square inches. Find the base and height. A = bh. 1. 1. 2. 2. 36 = (2 h )( h ). The height of the triangle is 6 inches, and the base is 6 2 = 12 inches . ANSWER. EXAMPLE 2.

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EXAMPLE 2

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  1. Algebra The base of a triangle is twice its height. The area of the triangle is 36 square inches. Find the base and height. A = bh 1 1 2 2 36 = (2h)(h) The height of the triangle is 6 inches, and the base is 6 2 = 12inches. ANSWER EXAMPLE 2 Solve for unknown measures Let h represent the height of the triangle. Then the base is 2h. Write formula. Substitute36forAand2hforb. 36 = h2 Simplify. 6 = h Find positive square root of each side.

  2. 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? EXAMPLE 3 Solve a multi-step problem Painting SOLUTION You can use a right triangle and a rectangle to approximate the area of the side of the barn.

  3. 338 = x = 26(18) + 1 (338 ) (338 ) 2 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. 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 =637 ft2

  4. 637 ft2 1.82 gal 1 gal 350 ft2 EXAMPLE 3 Solve a multi-step problem STEP 3 Determine how many gallons of paint you need. Use unit analysis. Round up so you will have enough paint. You need to buy 2 gallons of paint.

  5. 4. A parallelogram has an area of 153 square inches and a height of 17 inches. What is the length of the base? A = b h 153 = x 17 ANSWER Length of the base is 9 in. for Examples 2 and 3 GUIDED PRACTICE SOLUTION Let the length of the base bex Write formula. Substitute153forAand17forhand x forb. x = 9 Simplify.

  6. 5. 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? 338 = x for Examples 2 and 3 GUIDED PRACTICE 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. Solve for the positive value of x.

  7. = 26(18) + 1 (338 ) (338 ) 2 A = l b = 5 10 for Examples 2 and 3 GUIDED PRACTICE Find the approximate area of the side of the barn. STEP 2 Area = Area of rectangle + Area of triangle = 637 ft2 Find the area of window. STEP 3 Write formula. Substitute. = 50 ft2 Multiply.

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

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