Question

If the perimeter is 112,the width is 6times to get the length.what is the length?and the width?solve for an area

Answer 1

Answer:

The length of rectangle is 8  unit

The width of rectangle is 48  unit

The Area of rectangle is 384 unit²

Step-by-step explanation:

Given as :

The perimeter of rectangle = P = 112  unit

The width is 6 times the length

Let The length of rectangle = L  unit

Let The width of rectangle = W   unit

So, W = 6 × L      .........1

Let The Area of rectangle = A unit²

Now, According to question

∵ Perimeter of rectangle = 2 × Length + 2 × Breadth

Or, P = 2 × L + 2 × W

Or, 112 = 2 × L + 2 ×  6 × L              (from eq 1 )

Or, 112 = 2 × L + 12 × L

Or, 112 = 14 L

∴  L = $\dfrac{112}{14}$

i.e L = 8

So, The length of rectangle = L = 8  unit

Put the value of L into eq 1

∵ W = 6 × L

So, W = 6 × 8

i.e W = 48

So, The width of rectangle = W = 48  unit

Again

∵ The Area of rectangle = (Length × Width)  unit²

Or, A = L× W

Or, A = 8 × 48

i.e A = 384 unit²

So, The Area of rectangle = A =  384 unit²

Hence , The length of rectangle is 8  unit

The width of rectangle is 48  unit

The Area of rectangle is 384 unit²    Answer