Help on #14 **Problem 14: Use the Similar Figures to Find the Missing Value**In this problem, you are given two similar geometric figures with some dimensions labeled. 1. The smaller figure has a height of 14 units and a base of $ x $ units.2. The larger figure has a height of 32 units and a base of $ x+9 $ units.**Options to find $ x $:**- A: $ x = -16 $- B: $ x = 9 $- C: $ x = -16 $ (marked with a red cross, meaning it might be incorrect)- D: $ x = 7 $Since the figures are similar, their corresponding sides are proportional. This means the ratio of the corresponding sides of the two figures should be equal.Mathematically, we can set up the ratio as follows:\[\frac{14}{32} = \frac{x}{x+9}\]We can cross-multiply to solve for $ x $:\[14(x + 9) = 32x \\14x + 126 = 32x \\126 = 32x - 14x \\126 = 18x \\x = \frac{126}{18} \\x = 7\]Thus, the correct value of $ x $ is option D: $ x = 7 $.This problem demonstrates the concept of using proportions in similar figures to solve for unknown values.

Math

Geometry

#

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter9: Systems Of Linear Equations

Section9.5: Multiplication With The Addition-or-subtraction Method

Problem 31P

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Question

Help on #14

**Problem 14: Use the Similar Figures to Find the Missing Value**

In this problem, you are given two similar geometric figures with some dimensions labeled.

1. The smaller figure has a height of 14 units and a base of $ x $ units.
2. The larger figure has a height of 32 units and a base of $ x+9 $ units.

**Options to find $ x $:**
- A: $ x = -16 $
- B: $ x = 9 $
- C: $ x = -16 $ (marked with a red cross, meaning it might be incorrect)
- D: $ x = 7 $

Since the figures are similar, their corresponding sides are proportional. This means the ratio of the corresponding sides of the two figures should be equal.

Mathematically, we can set up the ratio as follows:
\[
\frac{14}{32} = \frac{x}{x+9}
\]

We can cross-multiply to solve for $ x $:
\[
14(x + 9) = 32x \\
14x + 126 = 32x \\
126 = 32x - 14x \\
126 = 18x \\
x = \frac{126}{18} \\
x = 7
\]

Thus, the correct value of $ x $ is option D: $ x = 7 $.

This problem demonstrates the concept of using proportions in similar figures to solve for unknown values.

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