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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 4: Q27. (page 139)

Find the values of $x$ and y.
27. ln equiangular $螖 ABC$ , $AB = 4 x - y, BC = 2 x + 3 y$ and $AC = 7$ .

Short Answer

Expert verified

The value of $x$ and $y$ is 2and 1 respectively.

Step by step solution

01

– Apply definition of equilateral triangle.

An equilateral triangle is a triangle which all the three sides are equal in length.

Therefore, in $螖 A B C, A B = B C = A C$ .

02

– Description of step.

Consider, $A B = A C$ .

Substitute $4 x 鈭� y$ for 7 and for $A C$ into $A B = A C$ and simplify.

$\begin{array}{l} 4 x 鈭� y = 7 \\ y = 4 x 鈭� 7 \end{array}$

03

– Description of step.

Consider, $B C = A C$ .

Substitute 7 for $A C$ and $2 x + 3 y$ for $B C$ into $B C = A C$ and simplify.

$2 x + 3 y = 7$

04

– Description of step.

Substitute $4 x 鈭� 7$ for $y$ into $2 x + 3 y = 7$ , to find the value of $x$ .

$\begin{array}{l} 2 x + 3 (4 x 鈭� 7) = 7 \\ 2 x + 12 x 鈭� 21 = 7 \\ 14 x = 28 \\ x = 2 \end{array}$

05

– Description of step.

Substitute 2 for $x$ into $y = 4 x 鈭� 7$ , to find the value of $y$ .

$\begin{array}{l} y = 4 脳 2 鈭� 7 \\ = 8 鈭� 7 \\ = 1 \end{array}$

Therefore, the value of $x$ and $y$ is 2 and 1 respectively.

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Most popular questions from this chapter

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