Presentation on theme: "Solve for unknown measures"— Presentation transcript:
1 Solve for unknown measures EXAMPLE 2Solve for unknown measuresAlgebra 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 = bh21Write formula.36 = (2h)(h)21Substitute 36 for A and 2h for b.36 = h2Simplify.6 = hFind positive square root of each side.The height of the triangle is 6 inches, and the base is = 12 inches.ANSWER
2 EXAMPLE 3Solve a multi-step problemPaintingYou 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?SOLUTIONYou can use a right triangle and a rectangle to approximate the area of the side of the barn.
3 (338 ) EXAMPLE 3 Solve a multi-step problem STEP 1 Find the length x of each leg of the triangle.262 = x2 + x2Use Pythagorean Theorem.676 = 2x2Simplify.338 = xSolve for the positive value of x.STEP 2Find the approximate area of the side of the barn.Area = Area of rectangle + Area of triangle= 26(18) + 12(338 )= 637 ft2
4 Solve a multi-step problem EXAMPLE 3Solve a multi-step problemSTEP 3Determine how many gallons of paint you need.637 ft 1.82 gal350 ft21 galUse unit analysis.Round up so you will have enough paint. You need to buy 2 gallons of paint.
5 Let the length of the base be x GUIDED PRACTICEfor Examples 2 and 3A parallelogram has an area of 153 square inches and a height of 17 inches. What is the length of the base?4.SOLUTIONLet the length of the base be xA = b hWrite formula.153 = x 17Substitute 153 for A and 17 for h and x for b.x = 9Simplify.ANSWERLength of the base is 9 in.
6 Find the length x of each leg of the triangle. GUIDED PRACTICEfor Examples 2 and 3WHAT 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.SOLUTIONYou can use a right triangle and a rectangle to approximate the area of the side of the barn.STEP 1Find the length x of each leg of the triangle.262 = x2 + x2Use Pythagorean Theorem.676 = 2x2Simplify.338 = xSolve for the positive value of x.
7 (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 triangle2(338 )= 26(18) + 1= 637 ft2STEP 3Find the area of window.A = l bWrite formula.=Substitute.= 50 ft2Multiply.
8 GUIDED PRACTICEfor Examples 2 and 3Find the approximate area you need to paint.STEP 4Area of side of barn – Area of window= 637 – 50= 587ANSWERYou need to paint an approximate area of 587 ft2.