Question

The length of a triangle is 93ft side a of the triangle is twice as long as side b side c is 3ft longer than dude a find the length of each side

Answer 1

The length of side a is 36 feet and side b is 18 feet and side c is 39 feet

Solution:

Given that length of triangle is 93 feet

Thus, perimeter of triangle = 93 feet

The three sides of triangle are a, b, and c

Side a of the triangle is twice as long as side b

side a = 2 times side b

a = 2b

`b = (a)/(2)` ---- eqn 1

Given that Side c is 3 ft longer than side a

side c = 3 + side a

c = 3 + a ------ eqn 2

The perimeter of triangle is given as:

p = a + b + c

Where a, b, c are the length of sides of triangle

Substitute eqn 1 and eqn 2 in above formula

`p = a + (a)/(2) + 3 + a`

Given that perimeter = 93

`93 = a + (a)/(2) + 3 + a\\\\93 = (2a + a + 6 + 2a)/(2)\\\\93 * 2 = 2a + a + 6 + 2a\\\\186 = 5a + 6\\\\5a = 186 - 6\\\\5a = 180\\\\a = 36`

Thus length of side a = 36 feet

Length of side b :

from eqn 1

`b = (36)/(2) = 18`

b = 18 feet

Length of side c:

From eqn 2,

c = 3 + 36 = 39

c = 39 feet

Thus length of side a is 36 feet and side b is 18 feet and side c is 39 feet