Question

Assume the triangles in the pair below are similar. Find the value of x. Enter only your numerical answer.

Answer 1

The answer is

$\frac{80}{11}$

Answer 2

Answer :

Given :

• Two triangles in pair are of same size and length.

Find :

• The value of x.

Solution:

Let ,

• The first triangle be 1∆
• The second triangle be 2∆

We know that,

• The triangles in the attachment are similar . That means the length of 1st triangle will be equal to that of the second.
• Thus , we can say that 1∆ = 2∆

Now,

• Both the triangles will have the same value.
• We can conclude that RT= BC
• That is RT = BC = 50

$\large{\boxed{\sf{Sum\;of\;triangle's\;side=180°}}}$

Taking this in mind solve for x,

$\rightarrow$ ST + SR + RT = 180°

$\rightarrow$ 70 + 11x - 4 + 60 = 180°

$\rightarrow$ 130 + 11x - 4 = 180°

$\rightarrow$ 124 + 11x = 180°

$\rightarrow$ 11x = 180 - 124

$\rightarrow$ 11x = 56

$\rightarrow$ x = $\dfrac{56}{11}$

$\rightarrow$ x = 5 (Approx)

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