Question

Rounded to the nearest tenth, what is the perimeter of the triangle?

a 30-60-90 triangle with a hypotenuse of length of 5 cm

A.
9.3 centimeters
B.
10.8 centimeters
C.
11.0 centimeters
D.
11.8 centimeters
E.
16.2 centimeters

Answer 1

The perimeter of the triangle is 11.72 cm

or ≈ 11.8 cm

Option C is correct.

Given:

• A 30-60-90 triangle with a hypotenuse of length of 5 cm.

To find:

• What is the perimeter of the triangle?
• A. 9.3 centimeters
• B. 10.8 centimeters
• C. 11.0 centimeters
• D. 11.8 centimeters
• E. 16.2 centimeters

Solution:

Concept/Formula to be used:

• Apply Pythagoras theorem, to find other sides, or
• Apply trigonometry ratio applications to find other sides.
• The side opposite to greater angle is greater.

Step 1:

Find the length of other sides.

According to the theorem of side length and angle,

AB= 2x and AC= x units.

Because,

$\bf \angle C=2\angle B$

Thus,

Apply Pythagoras theorem,

$\bf AB^{2} + AC^{2} = BC^2$

$4 {x}^{2} + {x}^{2} = 25$

$5 {x}^{2} = 25$

${x}^{2} = 5$

$x = \pm \sqrt{5}$

$\bf x = 2.24$

Neglecting the (-ve) value.

Thus,

Length of AC: 2.24 cm

Length of AB:4.48 cm

Step 2:

Find the perimeter of ∆ABC.

Perimeter of ∆ABC$\bf =AB+AC+BC$

$=2.24 + 4.48 + 5$

Perimeter of ∆ABC$\bf = 11.72 \: cm$

Thus,

The perimeter of triangle is 11.72 cm

or 11.8 cm (rounded to the nearest tenth)

Option C is correct.

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