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aliya0001 [1]
3 years ago
8

In isosceles ΔABC, AC = BC, AB = 6 in, CD ⊥ AB, and CD = 3 in. Find the perimeter of the isosceles triangle.

Mathematics
2 answers:
Nady [450]3 years ago
8 0

Answer:

4\sqrt{3}+6

Step-by-step explanation:

We know that the base is 6 and the altitude is \sqrt{3}

We need to know the sides of the triangle

The triangle is already divided into two by the altitude, the new base will be 3 because 6 divided by 2 is 3, and the side of the smaller triangle will be \sqrt{3}

So we use the pythagoream thereom: (\sqrt{3})^2+3^2=c^2

Now since we are squaring a square root, it goes back to 3, and we know 3^2 equals 9: 3+9= c^2

Now we solve: 12= c^2

                        \sqrt{12}=c

Now we know the side of the triangle ABC

Since it is an isosceles, both sides are  \sqrt{12}

Now we add all sides to get our perimeter: P= \sqrt{12}+\sqrt{12}+6

We know that \sqrt{12} + \sqrt{12} = \sqrt{24} = 4\sqrt{3} .......when we factor

Which is: 4\sqrt{3}+6

Hoochie [10]3 years ago
6 0

Answer:

Step-by-step explanation:

Consider the given triangle ABC, we have AC = BC, AB = 6 in, CD ⊥ AB, and CD = 3 in. Using ΔCDB, we have

(CB)^{2}=(CD)^{2}+(DB)^{2}

(CB)^{2}=(3)^{2}+(3)^{2}

CB=\sqrt{9+9}

CB=\sqrt{18}in

Therefore, CB=CA=\sqrt{18}in (Given)

Now, Perimeter of an isosceles triangle is given By: 2a+b

⇒2(\sqrt{18})+6=2(4.24)+6=8.48+6=14.48in

which is the required perimeter of isosceles triangle.

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