triangle abc is an isosceles triangle in which side ab = ac. what is the perimeter of triangle abc?

$5 + \sqrt{10}$ units
$10 + \sqrt{10}$ units
$10\sqrt{10}$ units
$50$ units

Question

triangle abc is an isosceles triangle in which side ab = ac. what is the perimeter of triangle abc?

$5 + \sqrt{10}$ units
$10 + \sqrt{10}$ units
$10\sqrt{10}$ units
$50$ units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Distance Formula", "Pythagorean Theorem", "Perimeter in Coordinate Plane" ], "new_concepts": [], "current_concepts": [ "Distance Formula", "Pythagorean Theorem", "Perimeter in Coordinate Plane" ] } ## Identify the coordinates of the vertices Using the *Distance Formula* and *Perimeter in Coordinate Plane* knowledge points $$ \begin{aligned} &A = (-4, -2)\ &B = (-1, 2)\ &C = (-4, 3) \end{aligned} $$ ## Calculate the length of side AC Using the *Distance Formula* knowledge point $$ \begin{aligned} d(A, C) &= \sqrt{(-4 - (-4))^2 + (3 - (-2))^2}\ &= \sqrt{0^2 + 5^2}\ &= 5 \end{aligned} $$ ## Calculate the length of side AB Using the *Distance Formula* and *Pythagorean Theorem* knowledge points $$ \begin{aligned} d(A, B) &= \sqrt{(-1 - (-4))^2 + (2 - (-2))^2}\ &= \sqrt{3^2 + 4^2}\ &= \sqrt{9 + 16}\ &= 5 \end{aligned} $$ ## Calculate the length of side BC Using the *Distance Formula* and *Pythagorean Theorem* knowledge points $$ \begin{aligned} d(B, C) &= \sqrt{(-4 - (-1))^2 + (3 - 2)^2}\ &= \sqrt{(-3)^2 + 1^2}\ &= \sqrt{9 + 1}\ &= \sqrt{10} \end{aligned} $$ ## Compute the perimeter of triangle ABC Using the *Perimeter in Coordinate Plane* knowledge point $$ \begin{aligned} \text{Perimeter} &= AB + AC + BC\ &= 5 + 5 + \sqrt{10}\ &= 10 + \sqrt{10} \end{aligned} $$

(A) $5 + \sqrt{10}$ units

(B) $10 + \sqrt{10}$ units

(C) $10\sqrt{10}$ units

(D) $50$ units

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Perimeter in Coordinate Plane" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the coordinates of the vertices

Calculate the length of side AC

Calculate the length of side AB

Calculate the length of side BC

Compute the perimeter of triangle ABC

Answer: