Question

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.

Answer 1

`\bf \underline{Given :-}`

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

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`\bf \underline{ To \: find:-}`

• Length of diagonal

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`\bf \underline{Solution:-}`

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.

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`\bigstar \boxed{ \rm Hypotenuse^2 = Base^2 + Perpendicular^2}`

Here :-

Hypotenuse = AD

Base = CD

Perpendicular = AC

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Therefore :-

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`\dashrightarrow\sf AD^2 =CD^2 + AC^2 \\`

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`\dashrightarrow\sf AD^2 =(130)^2 + (80)^2 \\`

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`\dashrightarrow\sf AD^2 =130 * 130 + (80)^2 \\`

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`\dashrightarrow\sf AD^2 =16900+ (80)^2 \\`

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`\dashrightarrow\sf AD^2 =16900+80 * 80 \\`

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`\dashrightarrow\sf AD^2 =16900+6400\\`

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`\dashrightarrow\sf AD^2 =23300\\`

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`\dashrightarrow\sf AD= √(23300) \\`

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`\dashrightarrow\bf AD =152.643 \: yds\\`

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