Area of Similar Triangles
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4. The ratio of height of small right triangle to bigger right triangle is $6 : 15$. The area of big triangle is $195\text{cm}^2$. Work out the area of small triangle.
This question includes visual content: Two right-angled triangles are displayed side-by-side. The smaller one on the left has its vertical leg labeled '6cm'. The larger one on the right has its vertical leg labeled '15cm'.
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Hi Gülen, let's work through this geometry problem together. We need to find the area of a small triangle based on its similarity to a larger one.
Similar Triangles: Areas and Ratios
First, we observe that the two right-angled triangles are similar shapes. This means the ratio between any two corresponding lengths is constant.
Let's find the scale factor for the lengths, which we will call k. We take the height of the small triangle over the height of the big triangle.
Substituting our given values, we get six over fifteen.
We can simplify this fraction by dividing both the numerator and the denominator by three. Six divided by three is two, and fifteen divided by three is five. So our scale factor is two-fifths.
Now, for similar figures, the ratio of their areas is equal to the square of the ratio of their lengths.
So, we need to square our scale factor of two-fifths.
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