Calculate Base Length in Isosceles Triangle: Area 24 cm², Height 8 units

Q: Why is the height 8 units and not something with x+2?

The problem states that DG = 8, which is the height from D perpendicular to base FE. The expression x+2 refers to segment GE, not the height!

Q: How do I know which side is the base?

The base is the side that the height is perpendicular to. Since DG is the height to side FE, then FE is our base.

Q: What does it mean that the triangle is isosceles?

An isosceles triangle has two equal sides. While this information helps us understand the triangle's shape, we don't need it to solve this particular area problem.

Q: Can I solve this without the area formula?

No, the area formula is essential here! Since you're given the area (24 cm²) and height (8), the area formula is the most direct way to find the base length.

Q: What if my answer doesn't match the multiple choice options?

Double-check your arithmetic! Make sure you used: $ 24 = \frac{1}{2} \times \text{base} \times 8 $, then solved: base = 24 ÷ 4 = 6 cm.

Area Formula with Isosceles Triangle Properties

Triangle DEF is an isosceles triangle

GE=X+2 DG=8

The area of the triangle is 24 cm².

DG is the height of the FE

Calculate the side FE

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Triangle DEF is an isosceles triangle

GE=X+2 DG=8

The area of the triangle is 24 cm².

DG is the height of the FE

Calculate the side FE

Step-by-step solution

To solve this problem, we will calculate the length of side $FE$ using the area formula for a triangle:

Step 1: Use the formula for the area of a triangle: $A = \frac{1}{2} \times \text{base} \times \text{height}$ .
Step 2: Substitute the given values into the formula.
We know that $A = 24 \, \text{cm}^2$ and $\text{height} = 8 \, \text{cm}$ .
Step 3: Set up the equation: $24 = \frac{1}{2} \times \text{base} \times 8$ .
Step 4: Simplify and solve for the base: $24 = \frac{8}{2} \times \text{base} \rightarrow 24 = 4 \times \text{base}$ .
Step 5: Solve for $\text{base}$ : $\text{base} = \frac{24}{4} = 6 \, \text{cm}$ .

Therefore, the side $FE$ of the triangle is 6 cm.

Final Answer

6 cm

Key Points to Remember

Essential concepts to master this topic

Area Formula: Use $A = \frac{1}{2} \times \text{base} \times \text{height}$ for triangles
Technique: Substitute known values: 24 = ½ × base × 8
Check: Verify with calculation: ½ × 6 × 8 = 24 ✓

Common Mistakes

Avoid these frequent errors

Using perimeter formula instead of area formula
Don't add the sides together to find area = wrong formula! Area isn't the same as perimeter - they measure completely different things. Always use A = ½ × base × height for triangle area calculations.

Practice Quiz

Test your knowledge with interactive questions

Angle A is equal to 30°.
Angle B is equal to 60°.
Angle C is equal to 90°.

Can these angles form a triangle?

FAQ

Everything you need to know about this question

Why is the height 8 units and not something with x+2?

The problem states that DG = 8, which is the height from D perpendicular to base FE. The expression x+2 refers to segment GE, not the height!

How do I know which side is the base?

The base is the side that the height is perpendicular to. Since DG is the height to side FE, then FE is our base.

What does it mean that the triangle is isosceles?

An isosceles triangle has two equal sides. While this information helps us understand the triangle's shape, we don't need it to solve this particular area problem.

Can I solve this without the area formula?

No, the area formula is essential here! Since you're given the area (24 cm²) and height (8), the area formula is the most direct way to find the base length.

What if my answer doesn't match the multiple choice options?

Double-check your arithmetic! Make sure you used: $24 = \frac{1}{2} \times \text{base} \times 8$ , then solved: base = 24 ÷ 4 = 6 cm.

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