Respuesta :
Answer:
Length of the longest side: 65 cm
Step-by-step explanation:
First side = x;
"Other side (with respect to first side)" = y;
Third side = z
When the first side is multiplied by 4, it is 10cm longer than 3 times the third side : 4x = 10 + 3z
We receive an equilateral triangle when one side increases by 11, and the other decreases by 11. Therefore when x + 11, and y - 11, x + 11 = z, and y - 11 = z.
x + 11 = z x - z = 11
y - 11 = z → y - z = 11
4x = 10 + 3z 4x - 3z = 10
Matrix:
[tex]\begin{bmatrix}1&-1&0&|&-11\\ 0&-1&1&|&11\\ 4&-3&0&|&10\end{bmatrix}[/tex]
If we reduce this matrix, our dimensions are 43, 54, and 65. Therefore the length of the longest side of the original triangle would be 65.
The sides of an equilateral triangle are equal.
The longest side of the original triangle is 65 cm
Let the sides of the original triangle be a, b and c.
From the question, we have:
[tex]\mathbf{4a = 10 + 3c}[/tex] --- the first side multiplied by 4, is 10 more than the third side multiplied by 3
The equations that relate the increment or decrement of the side lengths are:
[tex]\mathbf{a + 11 = c}[/tex]
[tex]\mathbf{b - 11 = c}[/tex]
Make a, the subject in [tex]\mathbf{a + 11 = c}[/tex]
[tex]\mathbf{a = c - 11}[/tex]
Substitute [tex]\mathbf{a = c - 11}[/tex] in [tex]\mathbf{4a = 10 + 3c}[/tex]
[tex]\mathbf{4(c - 11) = 10 + 3c}[/tex]
Open brackets
[tex]\mathbf{4c - 44 = 10 + 3c}[/tex]
Collect like terms
[tex]\mathbf{4c - 3c = 10 + 44}[/tex]
[tex]\mathbf{c = 54}[/tex]
Recall that: [tex]\mathbf{a = c - 11}[/tex]
So, we have:
[tex]\mathbf{a= 54 - 11}[/tex]
[tex]\mathbf{a= 43}[/tex]
Also, recall that: [tex]\mathbf{b - 11 = c}[/tex]
So, we have:
[tex]\mathbf{b - 11 = 54}[/tex]
[tex]\mathbf{b = 11 + 54}[/tex]
[tex]\mathbf{b = 65}[/tex]
So, we have:
[tex]\mathbf{a= 43}[/tex]
[tex]\mathbf{b = 65}[/tex]
[tex]\mathbf{c = 54}[/tex]
By comparing the side lengths, we have:
The longest side of the original triangle is 65 cm
Read more about equilateral triangles at:
https://brainly.com/question/3461022
