A student said thst the distance between (-5,7) and (3,7) is 2 unitsis the student correct?

Mathematics

1 answer:

Usimov [2.4K]2 years ago

3 0

No.

The distance is |-5 -3| = 8 units. (Y-coordinates are the same, so the distance is measured entirely in the x-direction. Distance is non-negative.)

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A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 88 feetfeet less than th

Y_Kistochka [10]

Answer: The length of the ladder is 20 feet.

Step-by-step explanation:

Given : A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 8 feet less than the length of the ladder.

Mathematically,

Let x be the length of the ladder then

Distance from ground to the top of the ladder = x- 8

If distance from the bottom of the ladder to the building is 16 feet.

Since ground makes right angle with building , so the triangle made by ladder should be a right triangle.

By Pythagoras theorem of right triangle , we hae

$(Hypotenuse)=(Perpendicular)^2+(Base)^2$

$\Rightarrow\ x^2=(x-8)^2+16^2\\\\\Rightarrow\ x^2=x^2+64-16x+256\ [\text{Using identity :} (a-b)^2=a^+b^2-2ab]\\\\\Rightarrow 0=-16x+320\\\\\Rightarrow\ 16x=320\\\\\Rightarrow\ x=\dfrac{320}{16}=20$