Question

The first side of a triangle is 7 cm shorter than twice the second side. The third side is 4 cm longer than the first

side. The perimeter is 80 cm. Find the length of each side.

Plz help me!

Answer 1

The length of the three sides are 18, 29 and 33

Explanation:

Let x represent the first side

Let y represent the second side

Let z represent the third side

The perimeter of the triangle is 80cm, which means adding the length of the three sides i.e.

x + y + z = 80cm ......... (eqn 1)

The first side (x) is 7cm shorter than two times (×2) the second side (y) i.e.

x = 2y - 7 ............ (eqn 2)

The third side (z) is 4 cm longer than the first

side (x) i.e.

z = 4 + x ................. (eqn 3)

If x + y + z = 80

We substitute eqn 3 for z

= x + y + 4 + x = 80

= 2x + y + 4 = 80

Next, we substitute eqn 2 for x;

= 2(2y-7) + y + 4 = 80

= 4y - 14 + y + 4 = 80

= 5y - 10 = 80

= 5y = 80 + 10

= 5y = 90

y = 18

If y = 18, we substitute the value of y in eqn 2;

x = 2(18) - 7

x = 36 - 7

x = 29

If x = 29 and y = 18, we substitute both values into eqn 1;

x + y + z = 80

= 29 + 18 + z = 80

= 47 + z = 80

= z = 80 - 47

z = 33

Thus; x, y and z representing the three sides are 29, 18 and 33 respectively.

Answer 2

The sides have lengths: 29,18, and 33

Explanation:

Let the first side have a f (meters);

the second side a length of s (meters)

and the third side a length of t (meters)

The first side of a triangle is 7 cm shorter than twice the second side.

f=2s-7

2s=f+7 Get b by itself by dividing by 2

s=(f+7)/2

The third side is 4 cm longer than the first side.

t=f+4

The perimeter is 80 cm.

f + s + t = 80

Replace s & t using the above equations

f+(f+7)/2+(f+4)=80 get rid of that annoying fraction, multiply by 2, results

2f + (f+7) + 2(f+4) = 2(80)

2f + f + 7 + 2f + 8 = 160 Combine like terms a's and constant

5f + 15 = 160 Subtract 15

5f = 145 Divide 5

f=29 is side f then

s=(29+7)/2 Add 29 and 7 together

s=36/2

s=18 is side s and

t= 20+4

t=33 is side t

To double check to make sure they add to 80

29+18+33=80