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DanielleElmas [232]
3 years ago
7

4 Consider the triangle below.

Mathematics
1 answer:
Maurinko [17]3 years ago
6 0
<h2>=>> <u>Solution (part A</u>) :</h2>

Given :

▪︎Triangle AMG is an isosceles triangle.

▪︎Measure of segment AM = (x+1.4) inches

▪︎Measure of segment MG = (2x+0.1) inches

▪︎Measure of segment AG = (3x-0.4) inches

▪︎segment AG is the base of triangle AMG.

Since AG is the base of the isosceles triangle AMG, segment AM and segment MG will be equal.

Which means :

= \tt x + 1.4 = 2x + 0.1

= \tt x + 1.4 - 0.1 = 2x

=  \tt \: x + 1.3 = 2x

= \tt 1.3 = 2x - x

\color{plum} \hookrightarrow  \tt x = 1.3

Thus, the value of x = 1.3

Therefore :

▪︎The value of x = 1.3

<h2>=>> <u>Solution (Part B)</u> :</h2>

We know that :

▪︎The value of x = 1.3

Which means :

The length of the leg AM :

= \tt x + 1.4

= \tt 1.3 + 1.4

\color{plum} \tt leg \: AM= 2.7 \: inches

Thus, the length of the leg AM = 2.7 inches

The length of leg MG :

= \tt 2x + 0.1

=  \tt2 \times 1.3 + 0.1

= \tt 2.6 + 0.1

\color{plum} \tt\: leg \:MG = 2.7 \: inches

Thus, the length of the leg MG = 2.7 inches

Since the measure of the two legs are equal (2.7=2.7), we can conclude that we have found out the correct length of each leg.

Therefore :

▪︎Measure of leg AM = 2.7 inches

▪︎Measure of leg MG = 2.7 inches

<h2>=>> <u>Solution </u><u>(</u><u>part C</u><u>)</u> :</h2>

We know that :

Value of x = 1.3

Then, measure of the base AG :

=  \tt 3x - 0.4

= \tt 3 \times 1.3 - 0.4

= \tt 3.9 - 0.4

\color{plum}\tt \: Base  \: AG = 3.5 \:  inches

Thus, the measure of the base = 3.5 inches

Therefore :

▪︎ the length of base AG = 3.5 inches.

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