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 2 h. 1 A = 2 bh Write formula. 1 36 = 2 (2 h)(h) Substitute 36 for A and 2 h for b. 36 = h 2 Simplify. Find positive square root of each side. 6=h ANSWER The height of the triangle is 6 inches, and the base is 6 2 = 12 inches.
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.
EXAMPLE 3 STEP 1 Solve a multi-step problem Find the length x of each leg of the triangle. 262 = x 2 + x 2 Use Pythagorean Theorem. 676 = 2 x 2 Simplify. 338 = x STEP 2 Solve for the positive value of x. Find the approximate area of the side of the barn. Area = Area of rectangle + Area of triangle = 26(18) + 1 2 ( 338 ) = 637 ft 2
EXAMPLE 3 Solve a multi-step problem STEP 3 Determine how many gallons of paint you need. 637 ft 2 1 gal 2 1. 82 gal Use unit analysis. 350 ft Round up so you will have enough paint. You need to buy 2 gallons of paint.
GUIDED PRACTICE for Examples 2 and 3 4. A parallelogram has an area of 153 square inches and a height of 17 inches. What is the length of the base? SOLUTION Let the length of the base be x A=b h Write formula. 153 = x 17 x=9 Substitute 153 for A and 17 for h and x for b. Simplify. ANSWER Length of the base is 9 in.
GUIDED PRACTICE for Examples 2 and 3 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? 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 = x 2 + x 2 676 = 2 x 2 338 = x Use Pythagorean Theorem. Simplify. Solve for the positive value of x.
GUIDED PRACTICE STEP 2 for Examples 2 and 3 Find the approximate area of the side of the barn. Area = Area of rectangle + Area of triangle = 26(18) + 1 2 STEP 3 ( 338 ) = 637 ft 2 Find the area of window. A = l b Write formula. = 5 10 Substitute. = 50 ft 2 Multiply.
GUIDED PRACTICE STEP 4 for Examples 2 and 3 Find the approximate area you need to paint. Area of side of barn – Area of window = 637 – 50 = 587 ANSWER You need to paint an approximate area of 587 ft 2.
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