The perimeter of an isosceles triangle is 32

Perimeter of a Triangle Formula What is the formula for the perimeter of a triangle? Let’s find out. Let a, b, and c be the lengths of the three sides of a triangle. Perimeter of triangle $= a + b + c$ How to Find the Perimeter of a Triangle Step 1: Note down the lengths of all three sides of the given triangle. Ensure that the lengths are in the same unit. Step 2: Add the lengths of the three sides. Step 3: The sum represents the perimeter of the given triangle. Assign the same unit to the perimeter as the length of the sides. Perimeter of an Equilateral Triangle A triangle with three equal sides and three congruent angles $(60^\circ)$ is known as an Consider an equilateral triangle ABC whose each side measures “a” units. Perimeter of an equilateral triangle $= a + a + a = 3a$ So, how do you find the perimeter of a triangle with three equal sides? Simply multiply the length of the side by 3! Perimeter of an Isosceles Triangle A triangle with two equal sides is known as an Since two sides of a triangle are equal, we have $a = b$ Perimeter of an isosceles triangle $= a + a + c = 2a + c$ Perimeter of a Scalene Triangle A triangle in which all the sides have different lengths is known as a If the lengths of three sides are given by a, b, and c, then Perimeter of a Right-angled Triangle A triangle in which one interior angle is $90^\circ$ is called a right triangle. The side opposite to the $90^\circ$ angle is called a hypotenuse. The other two sides are termed as “legs” of th...

We can start out by creating an equation that can represent the information that we have. We know that the total perimeter is #32# inches. We can represent each side with parenthesis. Since we know other 2 sides besides the base are equal, we can use that to our advantage. Our equation looks like this: #(x+2)+(x)+(x) = 32#. We can say this because the base is #2# more than the other two sides, #x#. When we solve this equation, we get #x=10#. If we plug this in for each side, we get #12, 10 and 10#. When added, that comes out to a perimeter of #32#, which means our sides are right.

Let A B C be an isoceles triangle with perimeter 32 c m . We have, ratio of equal side to its base is 13 : 2 . Let sides of triangle be A B = A C = 3 x , B C = 2 x ∵ Perimeter of a triangle = 32 m Now , 3 x + 3 x + 2 x = 32 ⇒ 8 x + 32 ⇒ x + 4 ∴ A B = A C = 3 × 4 = 12 c m and B C = 2 x = 2 × 4 = 8 c m The sides of a triangle are a =12 cm, b=12 cm and C = 8 c m. ∴Semi-perimeter of an isosceles triangle, s = a + b + c 2 = 12 + 12 + 8 2 = 32 2 = 16 c m ∴ Area of an isosceles △ A B C = √ s ( s − a ) ( s − b ) ( s − c ) [ by Heron's formula ] = √ 16 ( 16 − 12 ) ( 16 − 12 ) ( 16 − 8 ) = √ 16 × 4 × 4 × 8 ⇒ = 4 × 4 × 2 √ 2 c m 2 = 32 √ 2 c m 2 Hence, the area of an isosceles triangle is 32 √ 2 c m 2.