Question

a square and an equilateral traingle have a side 4/3 find perimeter

Answer 1

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=>. Answer:

64√3 cm2

Explanation:

Let As be the area of the square, Ps be the perimeter of the square and as be the length of a side of the square. (All sides have equal lengths.)

Let At be the area of the triangle, Pt be the perimeter of the triangle and at be the length of a side of the triangle. (All sides have equal lengths.)

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1) As we know the length of the diagonal of the square, we can compute the length of a side of the square using the Pythagoras formula:

a2s+a2s=d2

⇒2a2s=(12√2)2

⇒a2s=122

⇒as=12cm

2) Knowing the length of one side of the square (and thus knowing all lengths of a square), we can easily compute the square's perimeter:

Ps=12⋅4=48cm

3) We know that the square and the equilateral triangle have the same perimeter, thus

Pt=48cm

4) As all sides have the same length in an equilateral triangle, the length of one side is

at=Pt3=16 cm

5) Now, to compute the area of the equilateral triangle, we need the height h which can be computed with the Pythagoras formula again:

h2+(at2)2=a2t

⇒h2+82=162

⇒h2=192=64⋅3

⇒h=8√3cm

6) At last, we can compute the area of the triangle:

At=12⋅h⋅at=12⋅8√3⋅16=64√3 cm2

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