Question

Identify the similar triangles. Then find the value of x to the nearest tenth .

Answer 1

The similar triangles are Δ TUV ≅ Δ STV ≅ Δ SUT

The value of x is determined as 25.

How to calculate the value of x?

The value of x is calculated by applying the following method as shown below;

we will identify the similar triangles;

triangle TUV is similar to triangle STV and also similar to triangle SUT

Δ TUV ≅ Δ STV ≅ Δ SUT

The value of side length x is calculated as follows;

SV / ST = ST / SU

16 / 20 = 20 / x

16x = 20 x 20

16x = 400

x = 400 / 16

x = 25

Answer 2

Step 1

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

We will label the angles in the triangle thus;

Step 2

Identify the similar triangles in increasing order of size.

`\begin{gathered} The\text{ similat triangles are Triangle TUV, Triangle STV and Triangle SUT} \\ The\text{ similar triangles in increasing order are TUV\textasciitilde STV\textasciitilde SUT} \end{gathered}`

Answer;

`TUV\text{\textasciitilde STV\textasciitilde SUT}`

Step 3

Find the value of x using the ratio of similar triangles

`\begin{gathered} \frac{ST\text{ of medium triangle}}{SV\text{ of medium triangle}}=\frac{SU\text{ of biggest triangle\lparen x\rparen}}{ST\text{ of biggest triangle}} \\ (20)/(16)=(x)/(20) \\ 20(20)=16x \\ 400=16x \\ (16x)/(16)=(400)/(16) \\ x=25 \end{gathered}`

Answer;

`x=25`