A triangle has an area of 52 square inches and a height of 8 inches. Which equation can you use to find the length of the triangle's base, b? Choices: (A)52 = 1/2b(8 + 8) (B)52 = 1/2b(8) What is the length of the triangle's base? Write your answer as a whole number or decimal. Do not round. ____ inches

Identify Formula: First, let's identify the correct formula to use for calculating the base of the triangle. The area of a triangle is given by the formula Area = 1/2 * base * height. We know the area (52 square inches) and the height (8 inches), so we need to find the base, b. Evaluate Choices: Looking at the choices, (A) 52 = 1/2b(8 + 8) and (B) 52 = 1/2b(8). The correct formula for the area of a triangle is Area = 1/2 * base * height, which matches choice (B) because it simplifies to 52 = 1/2 * b * 8. Choice (A) incorrectly adds the height twice. Solve for Base: Now, using the correct formula from choice (B), we solve for b. Rearrange the equation 52 = 1/2 * b * 8 to find b. First, multiply both sides by 2 to get rid of the fraction: 104 = b * 8. Isolate Base: Next, divide both sides by 8 to isolate b: b = 104 / 8. Calculate Base: Calculate b: b = 13.

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A triangle has an area of $52\,\text{square inches}$ and a height of $8\,\text{inches}$ . Which equation can you use to find the length of the triangle's base, $b$ ? $\newline$ Choices: $\newline$ (A) $52 = \frac{1}{2}b(8 + 8)$ $\newline$ (B) $52 = \frac{1}{2}b(8)$ $\newline$ What is the length of the triangle's base? $\newline$ Write your answer as a whole number or decimal. Do not round. $\newline$ ____ inches

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Math Problems

Grade 6

Area of quadrilaterals and triangles: word problems

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Q. A triangle has an area of

52\,\text{square inches}

and a height of

8\,\text{inches}

. Which equation can you use to find the length of the triangle's base,

b

\newline

Choices:

\newline

(A)

52 = \frac{1}{2}b(8 + 8)

\newline

(B)

52 = \frac{1}{2}b(8)

\newline

What is the length of the triangle's base?

\newline

Write your answer as a whole number or decimal. Do not round.

\newline

____ inches

Identify Formula: First, let's identify the correct formula to use for calculating the base of the triangle. The area of a triangle is given by the formula $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ . We know the area ( $52$ square inches) and the height ( $8$ inches), so we need to find the base, $b$ .
Evaluate Choices: Looking at the choices, (A) $52 = \frac{1}{2}b(8 + 8)$ and (B) $52 = \frac{1}{2}b(8)$ . The correct formula for the area of a triangle is $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ , which matches choice (B) because it simplifies to $52 = \frac{1}{2} \times b \times 8$ . Choice (A) incorrectly adds the height twice.
Solve for Base: Now, using the correct formula from choice (B), we solve for $b$ . Rearrange the equation $52 = \frac{1}{2} \times b \times 8$ to find $b$ . First, multiply both sides by $2$ to get rid of the fraction: $104 = b \times 8$ .
Isolate Base: Next, divide both sides by $8$ to isolate $b$ : $b = \frac{104}{8}$ .
Calculate Base: Calculate $b$ : $b = 13$ .