Question

If side of an equilateral triangle is equals to diagonal of the square, whose side a units then area of an
equilateral triangle is​

Answer 1

Answer:

First of all draw 2 figures of a square and a equilateral triangle one after the another. Name them as square WXYZ and triangle ABC.

Now, let the value of a diagonal of a square be ‘x’ cm.

Thus, side of an equilateral triangle =’x’ cm.

So according to question we have:

Case1: area(square)=(side)^2

(Side)^2=6×(3)^1/2 cm^2

side×side=6×(3)^1/2 cm^2

Hence, side= ((6×3^1/2))^1/2 cm =(6×1.732)^1/2

Therefore, side= (10.392)^1/2 cm=3.22 cm.

case 2: Finally, applying the pythagorus theorem for 1 right angled triangle as WXZ, we have:

(P)^2+(B)^2=(H)^2; (3.22)^2+(3.22)^2=H^2

Since the value of H is taken as X(diagonal). Thus, we have:

((3.22)^2+(3.22)^2=X^2);(10.368+10.368=X^2)

(20.736=X^2); therefore, X=(20.736)^1/2

Finally, X=4.55 cm.

Part( b): Hence, (side(equilateral triangle))=x= 4.55 cm.

Therefore, area(equilateral triangle)=(3)^1/2×1/4×(side)^2

Thus, Area (equilateral triangle)=(3)^1/2×1/4×(4.55)^2 Sq. cm.=(1.732×20.702)/4 Sq. Cm=35.855/4 Sq. Cm= 8.9639 Sq. Cm or 8.964 Sq. Cm(approx) Ans

Step-by-step explanation:

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