Chapter 6: Q53. (page 292)

WRITING IN MATH
A rectangle is inscribed in an isosceles triangle as shown. Find the dimensions of the inscribed rectangle with maximum area. (Hint: Use similar triangles.)

Short Answer

Expert verified

Thedimensions are $5 \times 4$ inches

Step by step solution

Step 1. Given information

A figure is given as above

Step 2. Concept used

Make a quadratic equation by assuming one side as $x$. Find the maximum value of it and then find the value of dimensions.

Step 3. Calculation

Let $x =$ the length of the rectangle.

Then $8 - \frac{4}{5} x =$ the height of the rectangle.

$\begin{array}{l} = x (8) + x (- \frac{4}{5} x) \\ = 8 x - \frac{4}{5} x^{2} \\ = - \frac{4}{5} x^{2} + 8 x \end{array}$

$A (x)$ is a quadratic function with $a = - \frac{4}{5}, b = 8$ , and c=0. Since a<0, the function has a maximum value at the vertex of the graph.

$\begin{array}{l} = - \frac{8}{2 (- \frac{4}{5})} \\ = 5 \end{array}$

This means the maximum area occurs with length 5 inches and height $8 - \frac{4}{5} (5)$ or 4 inches.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

WRITING IN MATH
A rectangle is inscribed in an isosceles triangle as shown. Find the dimensions of the inscribed rectangle with maximum area. (Hint: Use similar triangles.)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Concept used

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Probability and Statistics

Mechanics Maths

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

WRITING IN MATHA rectangle is inscribed in an isosceles triangle as shown. Find the dimensions of the inscribed rectangle with maximum area. (Hint: Use similar triangles.)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Concept used

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Probability and Statistics

Mechanics Maths

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

WRITING IN MATH
A rectangle is inscribed in an isosceles triangle as shown. Find the dimensions of the inscribed rectangle with maximum area. (Hint: Use similar triangles.)