Question

The length of the equilateral triangle below are given in centimeters. a. Workout the value of x and y b. Workout the perimeter of the equilateral triangle c. Workout the the area of the equilateral triangle, giving your answer correct to 3sf(?)

Answer 1

Step-by-step explanation:

As it is an equilateral triangle, so all the sides of triangle are equal. Taking two sides and equating them:-

2y+1=x+3

2y=x+3-1

2y=x+2

x=2y-2

Placing the value of x in the equation of third side

2x-y=0

2(2y-2)-y=0

4y-4-y=0

3y-4=0

3y=4

y=4/3

To find the value of x place the value of y

$2x - y = 0 \\ 2x - \frac{4}{3} = 0 \\ \\ 2x = \frac{4}{3} \\ \\ x = \frac{4}{3 \times 2 } \\ \\ x = \frac{2}{3}$

Side of triangle:-

$x + 3 \\ \frac{2}{3} + 3 \\ \\ \frac{2 + 3 \times 3}{3} \\ \\ \frac{11}{3} cm$

Perimeter of triangle:-

3×side

3×11/3

11cm

Area of equilateral triangle:-

$\frac{ \sqrt{3} }{4} {s}^{2} \\ \\ \frac{ \sqrt{3} }{4} \times \frac{11}{3} \times \frac{11}{3} \\ \\ \frac{209.33}{36} \\ \\ 5.818 {cm}^{2}$

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