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.

36 = h2

Write formula.

Substitute 36 for A and 2h for b.

Simplify.

Let h represent the height of the triangle. Then the base is 2h.

36 = (2h)(h)21

A = bh21

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 3Solve a multi-step problem

Painting

You can use a right triangle and a rectangle to approximate the area of the side of the barn.

SOLUTION

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 3Solve a multi-step problem

338 = x Solve for the positive value of x.

Find the approximate area of the side of the barn.

STEP 1 Find the length x of each leg of the triangle.

262 = x2 + x2

676 = 2x2

Use Pythagorean Theorem.

Simplify.

STEP 2

Area = Area of rectangle + Area of triangle

= 26(18) + 12

(338 ) (338 ) = 637 ft2

EXAMPLE 3Solve 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.

637 ft2 1.82 gal

350 ft2 1 gal

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.

Let the length of the base be x

SOLUTION

A = b h

153 = x 17

x = 9

Write formula.

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

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

676 = 2x2

Use Pythagorean Theorem.

Simplify.

338 = x Solve for the positive value of x.

GUIDED PRACTICE for Examples 2 and 3

Find the approximate area of the side of the barn.

STEP 2

Area = Area of rectangle + Area of triangle

2 (338 ) (338 )= 26(18) + 1

STEP 3 Find the area of window.

Write formula.

Substitute.

A = l b

= 5 10

Multiply.

= 637 ft2

= 50 ft2

GUIDED PRACTICE for Examples 2 and 3

STEP 4 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 ft2.