Respuesta :
the area is 192 cm^2
the sides are 20 20 24 with the base being 24
to figure out the height you have to use Pythagorean theorem of the triangle cut in half so 12^2 + b^2 = 20^2
b= 16 = height
b*h* .5= area 16* 24* .5= 192
the sides are 20 20 24 with the base being 24
to figure out the height you have to use Pythagorean theorem of the triangle cut in half so 12^2 + b^2 = 20^2
b= 16 = height
b*h* .5= area 16* 24* .5= 192
The area of the given triangle is 192 cm² if it has 64cm of perimeter and a 6:5:5 ratio of the sides.
What is the perimeter and area of a triangle?
Consider a triangle that has three sides with measures a, b, and c.
Then,
The perimeter of a triangle = the sum of all sides i.e., (a + b + c)
and
The area of the triangle = 1/2 × b × h (b-base and h-height)
The height of a triangle can be calculated using the Pythagoras theorem.
Calculation:
Given that,
The perimeter of the triangle = 64 cm
The ratio of the sides is 6:5:5
Consider the measure of the side as x cm
Step 1: Calculating the value of x:
The sides are 6x, 5x, and 5x
Then the perimeter of the triangle = 6x + 5x + 5x
⇒ 64 = 16x
∴ x=4 cm
Step 2: Calculating the sides:
The sides are,
6x = 6 × 4
= 24 cm
5x = 5 × 4
= 20 cm
5x = 5 × 4
= 20 cm
Step 3: Applying Pythagoras theorem for finding the height:
The height can be calculated from the mid-point of the base, the triangle gets divided into right-angled triangles.
The highest measure of the sides is 24. So, consider it as the base for the triangle. The triangle is shown in the figure below.
So, D is the mid-point on the base and divides the triangle into two right triangles.
Thus, we can write
[tex]c^{2}=h^2+(a/2)^2[/tex]
On substituting the values,
⇒ (20)² = h² + (12)²
⇒ h² = 400 -144
⇒ h =√256
∴ h = 16 cm
Step 4: Finding the area:
Area = 1/2 × b × h (b-base of the entire triangle)
= 1/2 × 24 × 16
= 192 cm²
Thus, the area of the given triangle is 192 cm².
Learn more about the area and the perimeter of the triangle here:
https://brainly.com/question/21735282
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