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3 years ago

15

A fence was build arpund a square yard. It took 500 feet² of lumber to build the fence. The fence is five feet tall. What is the

area of the yard inside the fence?

1 answer:

Flauer [41]3 years ago

5 0

Answer:

625 square feet

Step-by-step explanation:

The length of the fence is its area divided by its height:

A = LW

500 ft² = L(5 ft)

(500 ft²)/(5 ft) = 100 ft = L

This encloses a square, so the side of the square is 1/4 of this length:

side = (100 ft)/4 = 25 ft

The yard's area is the square of the length of its side dimension:

yard area = (25 ft)² = 625 ft²

The area of the yard inside the fence is 625 square feet.

_____

<em>Comment on units</em>

If you keep units with numbers, you know that dividing 500 ft² by 5 ft will give a measure of 100 ft. This is a linear measure, not an area measure, so tells you that this is <em>not the answer</em> to the question of yard area.

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The coordinates G(7,3), H(9, 0), (5, -1) form what type of polygon?

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Answer:

Is an acute triangle

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

G(7,3), H(9, 0), I(5, -1)

step 1

Find the distance GH

substitute in the formula

$d=\sqrt{(0-3)^{2}+(9-7)^{2}}$

$d=\sqrt{(-3)^{2}+(2)^{2}}$

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step 2

Find the distance IH

substitute in the formula

$d=\sqrt{(0+1)^{2}+(9-5)^{2}}$

$d=\sqrt{(1)^{2}+(4)^{2}}$

$IH=\sqrt{17}\ units$

step 3

Find the distance GI

substitute in the formula

$d=\sqrt{(-1-3)^{2}+(5-7)^{2}}$

$d=\sqrt{(-4)^{2}+(-2)^{2}}$

$GI=\sqrt{20}\ units$

step 4

Verify what type of triangle is the polygon

we know that

If applying the Pythagoras Theorem

$c^{2}=a^{2}+b^{2}$ ----> is a right triangle

$c^{2}> a^{2}+b^{2}$ ----> is an obtuse triangle

$c^{2}< a^{2}+b^{2}$ ----> is an acute triangle

where

c is the greater side

we have

$c=\sqrt{20}\ units$

$a=\sqrt{17}\ units$

$b=\sqrt{13}\ units$

substitute

$c^{2}= (\sqrt{20})^{2}=20$

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therefore

$c^{2}< a^{2}+b^{2}$

Is an acute triangle

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