Chapter 4: Q27. (page 139)

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

Short Answer

Expert verified

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

Step by step solution

– Apply definition of equilateral triangle.

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

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

– Description of step.

Consider, $A B = A C$ .

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

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

– 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.

$2 x + 3 y = 7$

– Description of step.

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

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

– Description of step.

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

$\begin{array}{l} y = 4 \times 2 - 7 \\ = 8 - 7 \\ = 1 \end{array}$

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

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.

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

Short Answer

Step by step solution

– Apply definition of equilateral triangle.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Mechanics Maths

Geometry

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Find the values ofx and y.27. ln equiangular ΔABC,AB=4x-y,BC=2x+3y and AC=7.

Short Answer

Step by step solution

– Apply definition of equilateral triangle.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Mechanics Maths

Geometry

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

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