"The perimeter of a triangle is 294cm. The sides are x + 2, 2x + 3, and 3x + 1. Find the length of each side of the triangle."

50cm, 99cm, 145cm

Step-by-step explanation:

The perimeter is just the distance around the triangle. We have all three sides.

So

(x+2) + (2x + 3) + (3x + 1) = 294

Combine like terms

6x + 6 = 294

Subtract 6 on both sides

6x = 288

Divide 6 on both sides

x = 48

So the sides are

x + 2 = 48 + 2 = 50 cm

2x + 3 = 2(48) + 3 = 96 + 3 = 99 cm

3x + 1 = 3(48) + 1  = 145 cm

Checking, first:

50 + 99 + 145 = 194 cm

Plug in x = 48 to the original equation.

48 + 2 + 2(48) + 3 + 3(48) + 1 = 294

48 + 2 + 96 + 3 + 144 + 1 = 294

294 = 294

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.