Q36. Write an algebraic expression to... [FREE SOLUTION]

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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 1: Q36. (page 13)

Write an algebraic expression to represent the area of the triangle. Then evaluate it to find the area when $h = 12$ inches

Short Answer

Expert verified

The algebraic expression for the area is $\frac{h^{2}}{2} + 3 h$ and when $h = 12 鈥塱苍肠丑别蝉$ , the area is $A = 108 {鈥塱苍肠丑别蝉}^{2}$ .

Step by step solution

Step 1. Apply the formula.

The formula for the area of a triangle given by

$\frac{1}{2} 脳产补蝉别脳丑别颈驳丑迟$

Step 2. Example of finding the area of a triangle.

If the height of a triangle is $3 h + 2$ and the base of the triangle is $\frac{2}{h} + 1$ then the area is given by $\frac{1}{2} 脳产补蝉别脳丑别颈驳丑迟鈥�=鈥� \frac{1}{2} 脳 (3 h + 2) 脳 (\frac{2}{h} + 1)$ .

When $h = 2 鈥塱苍肠丑别蝉$ , the area of the triangle is given by

$\begin{array}{l} = \frac{1}{2} 脳 ((3 脳 2) + 2) 脳 (\frac{2}{2} + 1) \\ = \frac{1}{2} 脳 (6 + 2) 脳 (1 + 1) \\ = \frac{1}{2} 脳 8 脳 2 \\ = 8 {鈥塱苍肠丑别蝉}^{2} 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� \end{array}$

Step 3. Calculation using formula.

As the given right-angled triangle has height h and base h+6, so the area of a triangle is

$\begin{array}{l} A = \frac{1}{2} 脳 h 脳 (h + 6) \\ A = \frac{1}{2} (h^{2} + 6 h) \\ A = \frac{h^{2}}{2} + 3 h \end{array}$

Now, if $h = 12 鈥塱苍肠丑别蝉$ , the area is

$\begin{array}{l} A = \frac{{(12)}^{2}}{2} + 3 (12) \\ A = \frac{12 脳 12}{2} + 36 \\ A = 6 脳 12 + 36 \\ A = 72 + 36 \\ A = 108 {鈥塱苍肠丑别蝉}^{2} \end{array}$

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91影视

Write an algebraic expression to represent the area of the triangle. Then evaluate it to find the area when $h = 12$ inches

Short Answer

Step by step solution

Step 1. Apply the formula.

Step 2. Example of finding the area of a triangle.

Step 3. Calculation using formula.

One App. One Place for Learning.

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91影视

Write an algebraic expression to represent the area of the triangle. Then evaluate it to find the area when h=12inches

Short Answer

Step by step solution

Step 1. Apply the formula.

Step 2. Example of finding the area of a triangle.

Step 3. Calculation using formula.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Pure Maths

Logic and Functions

Decision Maths

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Write an algebraic expression to represent the area of the triangle. Then evaluate it to find the area when $h = 12$ inches