the perimeter of an isosceles triangle is 32 cm. the base is 2cmlonger than the length ofoneofthecongruentside

Question

what is the number of square centimeters in the area of the triangle

Answer 1

Now that the first answer established that the side lengths are 12, 10, and 10:

Area = 1/2 base * height, and base is 12.

For the height, draw a line down the middle of the triangle, from the top to the base. That divides the triangle into two right triangles. For each one, its base is b=6, and the hypotenuse is c=10. The other side is the height h. By the Pythagorean theorem, b^2+h^2=c^2, or 6^2+h^2=10^2.

You have 36+h^2=100, so h^2=100-36=64, and h=8.

Therefore, the height of the entire triangle is 8, and the area is (1/2)12*8=48.

Answer 2

METHOD 1:

Perimeter = sum of all sides.
Isosceles triangle means two of the sides are equal.
Let x be the length of one of the congruent sides.
Base = 2+x.
Side lengths are x, x, 2+x.
x + x + (2+x) = 32
3x + 2 = 32
3x = 30
x = 10

So, you're dealing with a triangle with side lengths 10, 10, 12 (base).

Now, find the area and you're set.

Draw a symmetric triangle with base = 12 and two sides = 10 meeting at the top.
Cut it in half by drawing dotted line down the middle.
This dotted line is the height.
Use Pythagorean theorem to find the height.
Half of the base = 6.
6^2 + h^2 = 10^2
Therefore, h = 8.

Now, finally:
Area = (1/2) * b * h
= (1/2) * 12 * 8
= 6 * 8
= 48 square centimeters


METHOD 2:
WARNING: You should probably not use this in school, but it's sometimes useful.

There is a another sneaky formula for calculating the area of ANY triangle, if you only know the side lengths. It's called Heron's formula, and it's:

Area = SqRt[s(s-a)(s-b)(s-c)]
Where a, b, c are the side lengths,
and s is half the perimeter [(a+b+c)/2].

s = 16, a = 10, b=10, c=12
Area = SqRt[16(16-10)(16-10)(16-12)]
= SqRt(16 * 6 * 6 * 4)
= SqRt(2304) = 48

Answer 3

Per the answer above, the triangles sides are 10, 10 and 12. Draw a picture of this, putting the 12 on the bottom. If you draw a line from the vertex to the middle of the 12 cm side, you will have a right triangle on each side with a base of 6 and a hypothenus of 10. Since a^2 + b^2 = c^2, you can calculate the height of the triangle to be 8. Now you know the base length (12) and the height length (8) and you can find the area.

Answer 4

Perimeter = sum of all sides
Isosceles triangle means two of the sides are equal
Let x be the length of one of the congruent sides.
Base = 2+x
Side lengths are x, x, 2+x
x + x + (2+x) = 32
3x + 2 = 32
3x = 30
x = 10

So, you're dealing with a triangle with side lengths 10, 10, 12.

Now, find the area and you're set.

Draw a triangle with base = 12 and sides = 10.
Cut it in half by drawing dotted line down the middle.
Use Pythagorean theorem to find the height.
Height = 8

please

Answer 5

A=1/2 bh

x+2 +x+x=32 3x=30 x=10 base=12, h=sqrt(10^2-6^2) =8

A=6*8=48 sq cm

Answer 6

P = 2x + b
b = x + 2

32 = 2x + (x + 2)
32 = 2x + x + 2
32 = 3x + 2
3x = 30
x = 10

b = 10 + 2 = 12

The sides are 10cm, 10cm, and 12cm

Area = b * sqrt(4a^2 - b^2)/4

Area = 12 * sqrt(4(10)^2 - 12^2))/4
Area = 3 * sqrt(4(100) - 144))
Area = 3 * sqrt(400 - 144)
Area = 3sqrt(256)
Area = 3 * 16
Area = 48

ANS : 48cm^2

Answer 7

32+32+34=98 cm

Answer 8

2x+(x+2)=32
3x+2=32
x=10cm and x+2=12cm(base)

x^2=6^2+h^2
100=36+h^2
h^2=64
h=8cm(height)

basexheight/2=12x8/2=48 square cm