For all your questions, big or small, IDNLearn.com has the answers you need. Our experts provide prompt and accurate answers to help you make informed decisions on any topic.
Sagot :
To solve for the lengths of the sides of the isosceles triangle, let's denote the length of the base by [tex]\( b \)[/tex] meters. Consequently, the length of each leg of the triangle is [tex]\( b + 4 \)[/tex] meters since the legs are 4 meters longer than the base.
The perimeter of a triangle is the sum of the lengths of all its sides. For this isosceles triangle, the perimeter comprises the base and the two equal legs. Hence, the perimeter [tex]\( P \)[/tex] can be expressed as:
[tex]\[ P = b + 2(b + 4) \][/tex]
We know that the perimeter of the triangle is 44 meters. Substituting 44 for [tex]\( P \)[/tex], we get:
[tex]\[ 44 = b + 2(b + 4) \][/tex]
Now, let's solve this equation step by step to find the value of [tex]\( b \)[/tex]:
Step 1: Expand the equation:
[tex]\[ 44 = b + 2b + 8 \][/tex]
Step 2: Combine the [tex]\( b \)[/tex] terms on the right-hand side:
[tex]\[ 44 = 3b + 8 \][/tex]
Step 3: Isolate the term containing [tex]\( b \)[/tex] by subtracting 8 from both sides of the equation:
[tex]\[ 44 - 8 = 3b \][/tex]
[tex]\[ 36 = 3b \][/tex]
Step 4: Solve for [tex]\( b \)[/tex] by dividing both sides by 3:
[tex]\[ b = \frac{36}{3} \][/tex]
[tex]\[ b = 12 \][/tex]
The length of the base [tex]\( b \)[/tex] is therefore 12 meters.
Next, we find the length of each leg. Since each leg is [tex]\( b + 4 \)[/tex]:
[tex]\[ \text{Leg} = 12 + 4 \][/tex]
[tex]\[ \text{Leg} = 16 \][/tex]
Now, we verify the result by calculating the perimeter of the triangle using these side lengths:
[tex]\[ \text{Perimeter} = \text{Base} + 2 \times \text{Leg} \][/tex]
[tex]\[ \text{Perimeter} = 12 + 2 \times 16 \][/tex]
[tex]\[ \text{Perimeter} = 12 + 32 \][/tex]
[tex]\[ \text{Perimeter} = 44 \][/tex]
Thus, the perimeter matches the given value, confirming that our solution is correct.
Therefore, the lengths of the sides of the triangle are:
- Base: 12 meters
- Each leg: 16 meters
The perimeter of a triangle is the sum of the lengths of all its sides. For this isosceles triangle, the perimeter comprises the base and the two equal legs. Hence, the perimeter [tex]\( P \)[/tex] can be expressed as:
[tex]\[ P = b + 2(b + 4) \][/tex]
We know that the perimeter of the triangle is 44 meters. Substituting 44 for [tex]\( P \)[/tex], we get:
[tex]\[ 44 = b + 2(b + 4) \][/tex]
Now, let's solve this equation step by step to find the value of [tex]\( b \)[/tex]:
Step 1: Expand the equation:
[tex]\[ 44 = b + 2b + 8 \][/tex]
Step 2: Combine the [tex]\( b \)[/tex] terms on the right-hand side:
[tex]\[ 44 = 3b + 8 \][/tex]
Step 3: Isolate the term containing [tex]\( b \)[/tex] by subtracting 8 from both sides of the equation:
[tex]\[ 44 - 8 = 3b \][/tex]
[tex]\[ 36 = 3b \][/tex]
Step 4: Solve for [tex]\( b \)[/tex] by dividing both sides by 3:
[tex]\[ b = \frac{36}{3} \][/tex]
[tex]\[ b = 12 \][/tex]
The length of the base [tex]\( b \)[/tex] is therefore 12 meters.
Next, we find the length of each leg. Since each leg is [tex]\( b + 4 \)[/tex]:
[tex]\[ \text{Leg} = 12 + 4 \][/tex]
[tex]\[ \text{Leg} = 16 \][/tex]
Now, we verify the result by calculating the perimeter of the triangle using these side lengths:
[tex]\[ \text{Perimeter} = \text{Base} + 2 \times \text{Leg} \][/tex]
[tex]\[ \text{Perimeter} = 12 + 2 \times 16 \][/tex]
[tex]\[ \text{Perimeter} = 12 + 32 \][/tex]
[tex]\[ \text{Perimeter} = 44 \][/tex]
Thus, the perimeter matches the given value, confirming that our solution is correct.
Therefore, the lengths of the sides of the triangle are:
- Base: 12 meters
- Each leg: 16 meters
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Thank you for visiting IDNLearn.com. We’re here to provide accurate and reliable answers, so visit us again soon.