The wheel of a car has an outer radius of 28 cm. Calculate how far the car travels after one complete Class 9

The wheel of a car has an outer radius of 28 cm. Calculate how far the car travels after one complete Class 9

Question 1.

The wheel of a car has an outer radius of 28 cm. Calculate how far the car travels after one complete turn of the wheel, and how many times the wheel turns during a journey of 1 km. Class 9

Solution:

Given:

Outer radius of wheel (r) = 28 cm

Distance travelled by wheel in one complete turn = Circumference of circle = 2πr

= 2 × $\frac{22}{7}$ × 28

= 44 × 4 = 176 cm

∴ Distance travelled by car in one turn = 176 cm

Now, car travelled a distance of 1 km.

∴ 1km = 100000 cm

Number of turns

$=\frac{\text { Total distance travelled }}{\text { Distance travelled in one turn }}=\frac{100000}{176}=568.18$

∴ Number of turns ≈ 568

Question 2.

Two rectangles have the same area and the same perimeter. Does this mean that they are congruent to each other? Class 9

Solution:

Let the two rectangles have dimensions

(l₁, b₁) and (l₂, b₂).

Both triangles have same perimeter

l₁ + b₁ = l₂ + b₂ ...(i)

Also, they have same area

l₁ · b₁ = l₂ · b₂ ... (ii)

From (i) and (ii)

l₁, b₁ and l₂, b₂ are roots of the same quadratic equation

x - (l₁ + b₁)x + l₁b₁ = 0

So {l₁, b₁} = {l₂, b₂} as sets.

Hence either l₁ = l₂ and b₁ = b₂, OR l₁ = b₂ and b₁ = l₂.

In both cases, the rectangles are congruent (a rectangle and its 90°-rotation are congruent).

Yes - two rectangles with the same area and the same perimeter must be congruent.