The ratio of an equal side of an isosceles triangle to it's base is 3: 4 and it's perimeter is 60 cm. find its area.

160.10 (2 dp.)

Step-by-step explanation:

So when you have ratio questions, similar to this one, you should always add up the parts.

This question actually involves many steps.

We are trying to find the length of all the sides first, we already know that the 3 sides add up to 60cm.

The triangle is made up of 3:3:4, as it has two equal sides and one base. The total parts is 3 + 3 + 4 = 10.

To find how much one part is. we divide the perimeter by the total parts

60/10 = 6

If one part equals 6, then we just multiply by the number of parts to find the entire length, this means that the sides equal 6 x 3 = 18 and the base is

6 x 4 = 24.

Now, we need to find the height in order to find the area of the triangle, to find the height we will be using Pythagoras theorem.

Pythagoras theorem states that a^2 + b^2 = c^2

If we split the triangle in half down the middle, we have a right angle triangle, we know the length of hypotenuse and one side.

The hypotenuse would be one of the equal sides of the isosceles triangle, which is 18cm, and the other side would be half of the base which is 24/2 = 12cm , as we are splitting the isosceles triangle down the middle.

Now we can use the theorem to find the height:

a = height

b = 12

c = 18

Formula:

h^2 + 12^2 = 18^2

rearrange and simplify:

18^2 - 12^2 = h^2

324 - 144 = h^2

180 = h^2

h = root 180 (we will leave this as a surd as it is not a perfect square)

Now that we know the height we can find the area, the formula of a triangle is half x base x height:

1/2 x 24 x root 180

= 160.10 (2 dp.)

Hope this helps,

Cate

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