Question

The length and breadth of a rectangle are in the ratio
5:4. The length of the rectangle is equal to the slant
height of a cone of height 48cm and base perimeter
88cm. What is the area (in cm2) of the rectangle?
Hw​

Answer 1

Answer:

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Answer 2

Given: The length and breadth of a rectangle are in the ratio 5:4. The length of the rectangle is equal to the slant height of a cone of height 48cm and base perimeter 88 cm.

To find: Area of the rectangle

Solution: Let the length and breadth of the rectangle be 5x and 4x respectively.

Let the height of the cone be h, radius be r and slant height be l.

h= 48 cm

Base perimeter of cone= 2 π r

=> 88 = 2 × (22/7) × r

=> 88 × 7 / 44 = r

=> r = 2×7

=> r = 14 cm

Slant height of the cone is given by

$= \sqrt{ {h}^{2} + {r}^{2} }$

$= \sqrt{ {48}^{2} + {14}^{2} }$

$= \sqrt{2304 + 196}$

$= \sqrt{2500}$

= 50 cm

Since length of the rectangle is equal to slant height of cone, therefore length= 50 cm

Therefore,

5x = 50

=>x = 50/5

=> x = 10

Breadth of rectangle

= 4x

= 4 × 10

= 40 cm

Therefore, length of rectangle= 50 cm and breadth of rectangle= 40 cm

Area of rectangle

= Length× Breadth

= 50 × 40

$= 2000 \: {cm}^{2}$

Therefore, area of the rectangle is $2000 \: {cm}^{2}$.