Find the length of x in the similar triangles below. 4. Two triangles are ______ if one is the enlargement or…

Question

Find the length of x in the similar triangles below. 4. Two triangles are ______ if one is the enlargement or reduction of the other.

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Here are the solutions to the problems:

3. Find the length of x in the similar triangles below.
The two triangles are similar. We can set up a proportion using the lengths of their corresponding sides.

Identify corresponding sides.
The vertical side of the upper triangle is 4 cm.
The vertical side of the lower triangle is 1.5 cm.
The horizontal side of the upper triangle is 6 cm.
The horizontal side of the lower triangle is x cm.
Set up the proportion of corresponding sides.
$\frac{4 \text{ cm}}{1.5 \text{ cm}} = \frac{6 \text{ cm}}{x \text{ cm}}$
Cross-multiply to solve for x.
$4 \times x = 6 \times 1.5$ $4x = 9$
Divide by 4 to find x.
$x = \frac{9}{4}$ $x = 2.25$
The length of x is $\boxed{2.25 \text{ cm}}$ .

4. Two triangles are ______ if one is the enlargement or other.
Two triangles are similar if one is the enlargement or reduction of the other. This means their corresponding angles are equal and their corresponding sides are in proportion.

The missing word is $\boxed{similar}$ .

Find the length of x in the similar triangles below. 4. Two triangles are ______ if one is the enlargement or reduction of the other.

Step-by-step solution

Identify corresponding sides.

Set up the proportion of corresponding sides.

Cross-multiply to solve for x.

Divide by 4 to find x.

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