Question

12. The base of a triangle with an area of 36 squared inches is 4.2 inches. What is the area of a similar

Answer 1

The 4.2 inches base length and 36 in.² area of the given triangle and the 5.6 inches base length of the similar triangle gives the area of the similar triangle as 64 square inches

Which method can be used to find the area of the similar triangle given the dimensions?

Area of a triangle = (Base length × Height)/2

Area of the given triangle = 36 in.²

Base length of the given triangle = 4.2 inches

Base length of the similar triangle = 5.6 inches

Therefore;

Area of the given triangle = (Base length × Height)/2

Which gives;

36 = (4.2 × h)/2

Where;

h = Height of the given triangle

36 × 2 = 4.2 × h

$h = \mathbf{\frac{36 \times 2}{4.2}} = 17 \frac{1}{7}$

Height of the given triangle, h = 17+ 1/7

The ratio of corresponding sides of similar triangles are the same, which gives;

$\frac{5.6}{4.2} = \frac{h'}{17 \frac{1}{7}}$

Where;

h' = The height of the similar triangle

Which gives;

$h' = \frac{5.6}{4.2} \times 17 \frac{1}{7} = 22 \frac{6}{7}$

The area, A', of the similar triangle is therefore;

$A' = \frac{1}{2} \times 5.6 \times 22 \frac{6}{7} = 64$

• The area of the similar triangle A' = 64 in.²

The area can also be obtained using the scale factor of area as follows;

• (4.2/5.6)² = 36/A'

Which gives;

• A' = 64 square inches

Learn more about scale factors of calculations here:

brainly.com/question/25722260

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