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

$5 + \sqrt{10}$ units
$3\sqrt{10}$ units
$10 + \sqrt{10}$ units
15 units

Question

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

$5 + \sqrt{10}$ units
$3\sqrt{10}$ units
$10 + \sqrt{10}$ units
15 units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distance Formula" ], "new_concepts": [ "Perimeter of a Triangle" ], "current_concepts": [ "Distance Formula", "Perimeter of a Triangle" ] } ## Calculate the length of side AB $$ \begin{aligned} A &= (-1, 6) \ B &= (-1, 1) \ AB &= \sqrt{(-1 - (-1))^2 + (6 - 1)^2} = \sqrt{0^2 + 5^2} = 5 \end{aligned} $$ ## Determine the length of side AC $$ \begin{aligned} AC &= AB = 5 \end{aligned} $$ ## Calculate the length of side BC and the perimeter $$ \begin{aligned} C &= (2, 2) \ BC &= \sqrt{(2 - (-1))^2 + (2 - 1)^2} = \sqrt{3^2 + 1^2} = \sqrt{10} \ \text{Perimeter} &= AB + AC + BC = 5 + 5 + \sqrt{10} = 10 + \sqrt{10} \end{aligned} $$

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

(B) $3\sqrt{10}$ units

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

(D) 15 units

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Perimeter of a Triangle" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate the length of side AB

Determine the length of side AC

Calculate the length of side BC and the perimeter

Answer: