Are these two quantities inversely proportional? a.) The time it takes to drive 100 miles and the average driving speed b.) The lengths of sides of a rectangle if the perimeter is fixed c.) The lengths of sides of a rectangle if the are is fixed

A, B & C are inversely proportional.

Step-by-step explanation:

For two quantities like x and y to be inversely proportional, they are to be written as;

y ∝ 1/x

This means that if x increases, then y decreases and if x decreases, then y increases.

A) The time it takes to drive 100 miles and the average driving speed.

Now, formula for time in motion is;

Time = Distance/speed

Let's denote time as t and speed as v.

Thus;

t = 100/v

From this relationship, it's clear that when v increases, then t decreases and vice versa. Thus it is inversely proportional.

B) The lengths of sides of a rectangle if the perimeter is fixed.

Perimeter of a rectangle is given as;

P = 2(L + W)

Where L is length and W is width.

Now, if the perimeter is fixed, it means an increase in the length will lead to a decrease in the width and vice versa. Thus, it is inversely proportional

C) The lengths of sides of a rectangle if the area is fixed.

If the sides are x & y.

Then;

A = xy

A/x = y

This means that;

1/x ∝ y.

Thus, the sides will be inversely proportional.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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