Question

PLS I NEED GOOD EXPLANATION

A rectangle is three times as long as it is wide.if its perimeter is 56cm .find the width of the perimeter ​

Answer 1

width = 7 cm

Explanation:

let w be width then length = 3w

The opposite sides of a rectangle are congruent , then perimeter is

2w + 2(3w) = 56 , that is

2w + 6w = 56

8w = 56 ( divide both sides by 8 )

w = 7

That is width of rectangle is 7 cm

Answer 2

❆ Cᴏɴᴄᴇᴘᴛ :-

In this question, we will take the help of the branch of mathematics known as "Perimeter and area". We will also use "linear equation in one variable". Let's solve it!

`\sf \dag \: \red{Given :-}`

• Perimeter of a rectangle = 56 cm

Let the width be x

Therefore, the length will be 3x.

`\sf \pink{Formula \: used :-}`

`\boxed{ \red \bigstar \: { \sf \orange{perimeter \: of \: a \: rectangle \: = 2(length + breadth)}}}`

Now we will simply put the given values in the formula to get the required answer.

`\sf \longrightarrow \: 56 \: cm = 2(x + 3x) \\ \sf \longrightarrow \: 56 \: cm = 2x + 6x \: \: \: \\ \sf \longrightarrow \: 8x = 56 \: cm \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \longrightarrow \: x = (56 \: cm)/(8) = 7 cm`

`\sf \green{ \therefore \: width \: = x = 7 \: cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:} \\ \sf \green{ and \: length \: = 3x = 3 * 7 = 21 \: cm}`

I hope that helps :))