Question

The length of a rectangle is 5 more than twice the width. If the perimeter of th

rectangle is 34, what is the length?

Answer 1

l=length, w=width
l=2w+5
2l+2w=34
2l=4w+10 [here I just multiplied the first equation by two]
4w+10+2w=34 [substitute 4w+10 for 2l]
6w=24, w=4
remember l=2w+5 so l=2(4)+5=13

Answer: The length is 13.

Answer 2

Appropriate Question -:

The length of a rectangle is 5 more than twice the width. If the perimeter of the rectangle is 34 cm find the length?

Step-by-step explanation -:

In this question we are provided with the perimeter of the rectangle = 34 cm and it is given that the length of the rectangle is 5 more than the twice it's breadth and asked to find out the length of the rectangle.

`\small \orange{ \underline{\rm \blue{length \: of \: a \: rectangle \: is \: 5 \: more \: than \: twice \: the \: width.}}}`

Let us assume breadth as x then length = 2x +5

We know,

`\star \: \large\boxed{ \rm{ Perimeter_((rectangle)) = 2(length + breadth)}}`

Substituting the values we get

34 = 2(2x +5 + x)

→ 34 = 2(3x + 5)

→ 34 = 6x + 10

→ 34 - 10 = 6x

→ 24 = 6x

→
`(24)/(6)` = x

x = 4

Length = 2x + 5 = 2 × 4 + 5 = 8 + 5 = 13 cm

Breadth = x = 4cm

Length = 13 cm.