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