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Math  /  Geometry

QuestionGiven a triangle with side lengths: a=12 m, b=7.5 m, c=8 m.\text{Given a triangle with side lengths: } a = 12 \, \text{m}, \, b = 7.5 \, \text{m}, \, c = 8 \, \text{m}. \text{Find the perimeter and area of this triangle.}

Studdy Solution

STEP 1

What is this asking? We need to find the total length around the triangle (that's the perimeter!) and the space *inside* the triangle (that's the area!). Watch out! Don't just add all the numbers you see!
We need to figure out which ones are the actual sides of the *whole* triangle.

STEP 2

1. Find the perimeter
2. Find the area

STEP 3

Alright, perimeter time!
The perimeter is just the sum of all the side lengths of the triangle.
We've got a=12\text{a} = 12 m, b=7.5\text{b} = 7.5 m, and c=8\text{c} = 8 m.

STEP 4

**Add** those sides up! Perimeter=a+b+c=12+7.5+8\text{Perimeter} = a + b + c = 12 + 7.5 + 8

STEP 5

Perimeter=27.5 m\text{Perimeter} = 27.5 \, \text{m} So, the **perimeter** is 27.5\textbf{27.5} **m**!

STEP 6

Now for the area!
Notice that we have a *right* triangle (that little square in the corner tells us that!). That makes finding the area way easier.
The area of a right triangle is one-half the product of the lengths of the two sides that meet at the right angle.

STEP 7

In our triangle, those sides are c=8\text{c} = 8 m and b=7.5\text{b} = 7.5 m.
Let's plug those values into the area formula! Area=12⋅b⋅c=12⋅7.5⋅8\text{Area} = \frac{1}{2} \cdot b \cdot c = \frac{1}{2} \cdot 7.5 \cdot 8

STEP 8

Area=12⋅60\text{Area} = \frac{1}{2} \cdot 60

STEP 9

Area=30 m2\text{Area} = 30 \, \text{m}^2 Boom! The **area** of our triangle is 30\textbf{30} **square meters**!

STEP 10

The perimeter of the triangle is 27.527.5 m, and the area is 3030 m2^2.

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