Question

The perimeter of a triangle is 40. How much bigger is the longest side than the shortest ?

Answer 1

10

Explanation:

40=2a-3+2a+3a+1

Add like terms.

40=7a-2

Get 'a' by itself.

40(+2)=7a-2(+2) [2 cancels out]

42(÷7)=7a(÷7) [7 cancels out]

a=6

Plug in the answer for equations.

Biggest: 3(6)+1= 18+1= 19

Smallest: 2(6)-3= 12-3=9

Subtract the smallest from the biggest.

19-9=10

Answer 2

A=8cm (Shortest)

B= 14cm

C = 18 cm (longest)

The longest side is 10 cm bigger than the shortest side

Explanation:

Let sides of a triangle be,

A, B and C

A be the short side

and C be the longest side

Perimeter = Sum of all sides = A+B+C = 40 cm

Using information given:

The length of the longest side is four cm less than the sum of th lengths of the other sides. The length of the shortest side is four cm more than the difference between the lengths of the other sides.

C = (A+B) -4

A = 2 (C-B)

rearrange:

A+B+C = 40 ----------------Equation 1

A+B-C = 4 ------------------ Equation 2

A+2B-2C = 0 -------------------- Equation 3

Equation 1 + Equation 2 :

2 (A+B) = 44

A+B = 22 ,

put in Equation 1 :

22 + C = 40

C = 18 cm

As A+B = 22 ,

we can write :

A = 22 -B

Put in Equation 3

22 - B + 2B - 2C = 0

B-2C = - 22

B = - 22 + 2C

B = - 22 + 36

B =14 cm

put value of B in A+B = 22

A + 14 = 22

A = 8 cm

Results:

A=8cm

B= 14cm

C = 18 cm

Here A is the shortest and C is the longest side,

So C-A = 18 - 8 = 10cm

The longest side is 10 cm bigger than the shortest