Question

The ratio of the length and the width of a rectangle is 4 ∶ 3, and its perimeter is the same as the perimeter of a right-angled triangle whose sides containing the right angle are 7 cm and 24 cm long, What is the area of the rectangle?

• A. 192 sq.cm
• B. 176 sq.cm
• C. 204 sq.cm
• D. 180 sq.cm

Answer 1

Answer:

A. 192 sq.cm

Solution:

Given:

length : breadth = 4 : 3

right angled triangle sides = 7 cm and 24 cm

Formula used:

Perimeter of right angled triangle $=a+b+\sqrt{a^2+b^2}$

Perimeter of rectangle = 2 × (length + breadth)

Area of rectangle = length × breadth

Calculations:

Let the length and width of rectangle be 4x and 3x

Required perimeter of right angled triangle $=7+24+\sqrt{7^2+24^2}$

$=31+\sqrt{49+576}$

$=31+\sqrt{625}$

$=31+25$

= 56 cm (which is equal to the perimeter of rectangle)

Now, 56 = 2 × (4x + 3x)

=> 56 = 2 × 7x

=> x = 4

Required length(4x) = (4 × 4) = 16 cm and width(3x) = ( 3 × 4) = 12 cm

So, required area of rectangle = (16 × 12) = 192 sq.cm.

The answer is 192 sq.cm.