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defon
3 years ago
5

There is a L-shaped sidewalk that is 158 meters long. By cutting across the lawn, the

Mathematics
1 answer:
NikAS [45]3 years ago
7 0

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.

(Hypotenuse)^2=(height)^2+(base)^2

So,

⇒ (130)^2=x^2 +(158-x)^2

⇒ (130)^2=x^2+(158-x)(158-x)

⇒ 16900=x^2+24964-158x-158x+x^2

⇒ 16900 =2x^2-316x+24964

⇒ 2x^2+316x+24964-16900=0

⇒ 2x^2-316x+8064=0

⇒ x^2-158x+4032=0

Applying quadratic formula;

Quadratic formula : \frac{\pm b \sqrt{b^2-4ac} }{2a} 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

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