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Murrr4er [49]
3 years ago
12

A square and an equilateral triangle have equal perimeters. the area of the triangle is 

Mathematics
1 answer:
Ivenika [448]3 years ago
3 0

a - length of side of a square

t - length of side of a triangle

The perimeter of a square: P_S=4a

The perimeter of a triangle: P_T=3t

We have the area of a triangle: A_T=16\sqrt3\ cm^2

The formula of an area of an equilateral trinagle: A_T=\dfrac{t^2\sqrt3}{4}

Substitute:

\dfrac{t^2\sqrt3}{4}=16\sqrt3    <em>multiply both sides by 4</em>

t^2\sqrt3=64\sqrt3     <em>divide both sides by \sqrt3</em>

t^2=64\to t=\sqrt{64}\to t=8\ cm

The perimeter of a triangle: P_T=3(8)=24\ cm

Substitute to the formula of a perimeter of a square:

4a=24       <em>divide both sides by 4</em>

a=6\ cm

The formula of a diagonal of a square: d=a\sqrt2

Substitute:

d=6\sqrt2\ cm

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