Question

The length of rec triangle is three times its width it the perimeter is 84 find the length of rectangle​

Answer 1

Correct Question :-

The length of rectangle is three times of its width. If the perimeter is 84 cm , then find the length of the rectangle.

${ \huge{ \underline{ \underline{ \sf{ \green{GivEn : }}}}}}$

•The length of rectangle is three times of its width.

•The perimeter is = 84 cm

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• What's the length of the rectangle?

Formula to be used :-

• Perimeter of rectangle = 2 ( Length+Width)

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

Let the width of the rectangle be x cm.

Therefore, as per question

The length of rectangle is three times of its width.

Then, the width of the rectangle will be 3x cm.

Now, find the perimeter of the given rectangle.

We know,

Perimeter of rectangle = 2 ( Length+Width)

⟹ Perimeter = 2(3x+x) cm

⟹ Perimeter = 8x cm

According to the question :-

Given that,

The perimeter of the given rectangle is 84 cm.

Therefore,

8x = 84

⟹ x = 10.5

So, width of the rectangle is = 10.5 cm

Length of the rectangle is

= 3x

= 3 × 10.5

= 31.5 cm.

Hence, the length of the rectangle is 31.5 cm.

____________________________________________

Verification :-

Given that,

The perimeter of the given rectangle is 84 cm.

Where,

Length = 31.5 cm

Width = 10.5 cm

Perimeter = 84

⟹ 2(31.5+10.5)=84

⟹ 84 = 84

L.H.S = R.H.S

Hence, verified.