Question

The width of a rectangle is 2/5 its length. Find the dimensions if the perimeter is 42 meters.

length = 13m, Width = 8m.
not enough information.
length = 15m, Width = 6m.
length =1 11m, Width = 10m.

Answer 1

The formula to find the perimeter of a rectangle is P= 2(l+w). Substitute what we know in to the equation:

•42=2(l+(2/5l)). We can have width represented at (2/5l) because it’s 2/5 of the length. Now add them together to get a single coefficient for l.
•42= 2(7/5l). Multiply 7/5 by 2.
•42= (14/5l). Multiply both sides by the reciprocal of 14/5, which is 5/14, to get l by itself.
•l= 15.

Now that we know the value of l, we know that the length is 15m. To find the width, we multiply 15 by 2/5, which is 6. Therefore, the third option is correct because the length is 15m and the width is 6m.

Answer 2

the dimensions of rectangle are length = 15 m and width = 6 m

Explanation:

Given; The width of a rectangle is
`(2)/(5)` its length i.e,
`w=(2)/(5)l`

and perimeter of rectangle is 42 meters.

Perimeter(P)of a rectangle in meters is given by:

`P = 2(l+w)` ; where
`l` is the length of the rectangle and w is the width of the rectangle.

then, substitute the value of P =42 m and
`w=(2)/(5)l` in above formula we get;

`42 = 2(l+(2)/(5)l) =2 \cdot ((7)/(5)l)`

divide both side by 2 we get;

`21=(7)/(5)l`

On Simplify:

`l = (21 \cdot 5)/(7) =3 \cdot 5 =15` m

Now, substitute the value of
`l = 15` m in
`w=(2)/(5)l` to solve for w;

`w= (2)/(5) \cdot 15 =2 \cdot 3 =6` m

Therefore, the dimensions length = 15 m and width = 6 m