Q. 466 A triangular banner has an area ... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 466 (page 984)

A triangular banner has an area of $351$ square centimeters. The length of the base is two centimeters longer than four times the height. Find the height and length of the base.

Short Answer

Expert verified

The base is $54$ cm and height is $13$ cm.

Step by step solution

Step 1. Given information.

The length of the base is two centimeters longer than four times the height.

The area of a triangular banner is $351$ square centimeters.

Step 2. Find base and height of the triangle.

Let the height of the triangle is $h$ .

The length of the base is two centimeters longer than four times the height.

So, the required base is $b = 4 h + 2$ .

Step 3. Apply the formula of the area of a triangle.

$\begin{array}{rcl} A & = & \frac{1}{2} b h \\ 351 & = & \frac{1}{2} (4 h + 2) h 鈰� 鈰� (G i v e n A = 351) \\ 351 脳 2 & = & 4 h^{2} + 2 h \\ 4 h^{2} + 2 h & = & 702 \\ 4 h^{2} + 2 h - 702 & = & 0 \\ 2 (2 h^{2} + h - 351) & = & 0 \\ 2 h^{2} + h - 351 & = & 0 \end{array}$

Step 4. Apply the quadratic formula, h=-b±b2-4ac2a.

The standard form of the above equation is $2 h^{2} + h + (- 351) = 0$ .

$\begin{array}{rcl} h & = & \frac{- 1 卤 \sqrt{1^{2} - 4 脳 2 脳 (- 351)}}{2 脳 2} 鈰� 鈰� (a = 2, b = 1, c = - 351) \\ = & \frac{- 1 卤 \sqrt{1 + 2808}}{4} \\ = & \frac{- 1 卤 \sqrt{2809}}{4} \\ = & \frac{- 1 卤 53}{4} \end{array}$

Step 5. Now solve the equation for h.

$\begin{array}{rcl} h & = & \frac{- 1 + 53}{4} \\ = & \frac{52}{4} \\ = & 13 \end{array}$ and $\begin{array}{rcl} h & = & \frac{- 1 - 53}{4} \\ = & \frac{- 54}{4} \\ = & - 13.5 (r e j e c t e d, h e i g h t c a n' t b e n e g a t i v e) \end{array}$

Step 6. Simplified answer.

The required base is:

$\begin{array}{rcl} b & = & 4 h + 2 \\ = & 4 脳 13 + 2 \\ = & 52 + 2 \\ = & 54 c m \end{array}$

The height is $h = 13 c m$ .

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91影视

A triangular banner has an area of $351$ square centimeters. The length of the base is two centimeters longer than four times the height. Find the height and length of the base.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find base and height of the triangle.

Step 3. Apply the formula of the area of a triangle.

Step 4. Apply the quadratic formula, h=-b±b2-4ac2a.

Step 5. Now solve the equation for h.

Step 6. Simplified answer.

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91影视

A triangular banner has an area of 351square centimeters. The length of the base is two centimeters longer than four times the height. Find the height and length of the base.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find base and height of the triangle.

Step 3. Apply the formula of the area of a triangle.

Step 4. Apply the quadratic formula, h=-b±b2-4ac2a.

Step 5. Now solve the equation for h.

Step 6. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

A triangular banner has an area of $351$ square centimeters. The length of the base is two centimeters longer than four times the height. Find the height and length of the base.