Consider triangle ABC with AB = 4 cm and BC = 6 cm. If AB = AC, name the type of triangle and calculate its…

Question

Consider triangle ABC with AB = 4 cm and BC = 6 cm. If AB = AC, name the type of triangle and calculate its perimeter. Then, describe how to draw it.

ScanSolve AI Tutor · Accepted Answer

a) To name the type of triangle ABC:
The tick marks on sides AB and AC indicate that these two sides are equal in length. Given that side AB is $4 \text{ cm}$ , side AC must also be $4 \text{ cm}$ . A triangle with two equal sides is called an isosceles triangle.

b) To find the perimeter of triangle ABC:
The perimeter of a triangle is the sum of the lengths of its three sides.
Side lengths are:
AB = $4 \text{ cm}$
BC = $6 \text{ cm}$
AC = $4 \text{ cm}$ (since AB = AC)

Identify the lengths of all sides.
$AB = 4 \text{ cm}$ $BC = 6 \text{ cm}$ $AC = 4 \text{ cm}$
Calculate the perimeter by adding the lengths of the three sides.
$\text{Perimeter} = AB + BC + AC$ $\text{Perimeter} = 4 \text{ cm} + 6 \text{ cm} + 4 \text{ cm}$ $\text{Perimeter} = 14 \text{ cm}$
a) The type of triangle is an isosceles triangle.

b) The perimeter of triangle ABC is $\boxed{14 \text{ cm}}$ .

c) This part requires a physical drawing using a ruler and pencil, which cannot be performed here.

Consider triangle ABC with AB = 4 cm and BC = 6 cm. If AB = AC, name the type of triangle and calculate its perimeter. Then, describe how to draw it.

Step-by-step solution

Identify the lengths of all sides.

Calculate the perimeter by adding the lengths of the three sides.

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