Answer:
Each side of the L-shaped sidewalk is 126 m and 32m respectively.
Step-by-step explanation:
Given:
Total length of the sidewalk = 158 meters
Cutting across the lawn the distance = 130 meters
The L-shaped lawn will be treated as a right angled triangle.
So the 130 m distance is the hypotenuse here.
Let one side of the L-shaped lawn be 'x' meter so the another side will be (158-x) meters.
Applying Pythagoras formula.
[tex](Hypotenuse)^2=(height)^2+(base)^2[/tex]
So,
⇒ [tex](130)^2=x^2 +(158-x)^2[/tex]
⇒ [tex](130)^2=x^2+(158-x)(158-x)[/tex]
⇒ [tex]16900=x^2+24964-158x-158x+x^2[/tex]
⇒ [tex]16900 =2x^2-316x+24964[/tex]
⇒ [tex]2x^2+316x+24964-16900=0[/tex]
⇒ [tex]2x^2-316x+8064=0[/tex]
⇒ [tex]x^2-158x+4032=0[/tex]
Applying quadratic formula;
Quadratic formula : [tex]\frac{\pm b \sqrt{b^2-4ac} }{2a}[/tex] where a=1 and b=-158 and c=4032
So the value of x= 126 and 32.
The length of each side of the sidewalk is 'x'= 126 m and '(158-x)'='(158-126)'=32 m
