Question

The first side of a triangle is 4 inches longer then twice th second side the third side of a trianhle

Answer 1

Question:

The first side of a triangle is four inches longer than twice the

second side. The third side of the triangle is 5 inches shorter than

the sum of the other two sides. The perimeter is 72 inches. Find

the lengths of the three sides.

Answer:

The sides of the triangle are: 11.5, 27 and 33.5

Step-by-step explanation:

Let the first side be f, the second be s and the third be t.

So, we have:

$f =4 + 2s$

$t = f + s - 5$

$Perimeter = 72$

Required

Determine the length of the three sides

Perimeter is calculated as:

$Perimeter = f + t + s$

Substitute values for f and t

$Perimeter = 4+2s + f+s-5 + s$

$Perimeter = f+2s +s+s-5+4$

$Perimeter = f+4s-1$

Substitute values for f and Perimeter

$72 = 4+2s+4s-1$

$72 = 2s+4s-1+4$

$72 = 6s+3$

Collect Like Terms

$6s = 72 -3$

$6s = 69$

$s= 11.5$

$f =4 + 2s$

$f = 4 + 2 *11.5$

$f = 27$

$t = f + s - 5$

$t=27+11.5 - 5$

$t=33.5$

The sides of the triangle are: 11.5, 27 and 33.5