Please, help if you are good in math?

Question

The perimeter of a triangle is 54 cm. The longest side is 7cm less than the sum of the lengths of the other two sides. twice the shortest side is 3cm more than the longest side. Find the lengths of the sides.

Answer 1

Let's start by assigning meanings to variables:

x = shortest side
2x -3 = longest side

For the third side, we need to solve "longest side is 7 cm less than sum of other two sides":

longest side = third side + shortest side - 7
(2x - 3) = third side + (x) - 7
third side = 2x - x - 3 + 7
third side = x + 4

Perimeter = side 1 + side 2 + side 3
54 = (x) + (2x - 3) + (x + 4)
54 = 4x + 1
4x = 53
x = 53/4 = 13.25

Therefore, substitute x back into our definitions above and you get:

Shortest side = x = 13.25 cm
Longest side = 2x - 3 = 23.5 cm
Third side = x + 4 = 17.25 cm

Check your answer:

Does 13.25 + 23.5 + 17.25 = 54? Yes! therefore, correct!

Answer 2

find the three equation

a is the longest side , c the shortest

eq 1 a+b+c =54 comes from perimeter is sum of the sides

eq 2 a+7 = b+c

eq 3 a+3 =2c

if you replace b+c by a+7 in 1
you find 2a+7 = 54 a= 23.5

eq 3 26.5 = 2c c = 13.25

and b = 14.75 with any of equation

Answer 3

let say the three sides are of length a cm, b, and c cm

so a+b+c = 54 -- (i)

a be the longest side

(b+c)=7+a --- (ii)

c be the shortest side

2c=3+a -- (iii)


using (i) and (ii)

a+a+7=54
2a=54-7
a=23.5

from (iii)
2c=3+a
put the a value here
c= 12.75

and solve b in (ii)

b=7+a-2
b= 17.75

so three sides = 17.75, 12.75,23.5
and add them to make sure they equal to the perimeter.. \
yes, they do!

Answer 4

let the lengths of the 3 sides be L, M and S cm

L + M + S = 54 ................... (1)
L = M + S - 7 → L - M - S = -7 ................ (2a)
and M = L + 7 - S ................. (2b)
L + 3 = 2S → S = ½(L + 3) ......................... (3)

Equation (1) + equation (2a)
2L = 47
L = 23.5

From equation (3) S = 13.25

From equation (2b) M = 30.5 - 13.25 = 17.25

Check 23.5 + 17.25 + 13.25 = 54 YESSSSSSSSS!!!!!!!!!!!

So the lengths of the sides of the triangle are 23.5 cm, 17.25 cm and 13.25 cm

Answer 5

That's easy :)
Can't you do your own homework ?

Answer 6

23.50
13.25
17.25

Answer 7

a+b+c=54
c=a+b-7
2a=c+3
c=2a-3
a+b+2a-3=54
b=c-a+7
b=2a-3-a+7
b=a+4
a+a+4+2a-3=54
4a=53
a=13.25
c=2a-3=23.5
b=a+4=17.25
a+b+c=13.25+17.25+23.5=54
c=13.25+17.25-7=23.5
2a=23.5+3=26.5
a=13.25