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A soccer field is 80 yds wide and 130 yds long. Find the length of the diagonal of such a field. Give an exact answer as a radical expression and an approximation to three decimal places.

Sagot :

WindyMint

[tex] \bf \underline{Given :-}[/tex]

  • Width of soccer field = 80 yds
  • Length of soccer feild = 130 yds

[tex] \\ \\ [/tex]

[tex] \bf \underline{ To \: find:-}[/tex]

  • Length of diagonal

[tex] \\ \\ [/tex]

[tex] \bf \underline{Solution:-}[/tex]

Strongly recommend to keep up with Digram , as name of sides are based according to Digram.

As we know soccer feild is rectangle , therefore ∠A = ∠B = ∠C = ∠D = 90°

Now as we have to just find value of diagonal AD therefore just focus on triangle ACD.

we know ∠C = 90° , triangle ACD. is a right angled triangle.

[tex] \\ \\ [/tex]

[tex] \bigstar \boxed{ \rm Hypotenuse^2 = Base^2 + Perpendicular^2}[/tex]

Here :-

Hypotenuse = AD

Base = CD

Perpendicular = AC

[tex] \\ [/tex]

Therefore :-

[tex] \\ [/tex]

[tex] \dashrightarrow\sf AD^2 =CD^2 + AC^2 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow\sf AD^2 =(130)^2 + (80)^2 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow\sf AD^2 =130 \times 130 + (80)^2 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow\sf AD^2 =16900+ (80)^2 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow\sf AD^2 =16900+80 \times 80 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow\sf AD^2 =16900+6400\\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow\sf AD^2 =23300\\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow\sf AD= \sqrt{23300} \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow\bf AD =152.643 \: yds\\ [/tex]

[tex] \\ \\ [/tex]

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