Question

Question #df4d2

Answer 1

`"area "=64" square metres"`

Explanation:

`• " perimeter "=(2xx"length")+(2xx"breadth")`

`• " area "="length "xx" breadth"`

`"let breadth "=b`

`"then length "=5b-4larr"4 less than 5 times breadth"`

`"perimeter "=2b+2(5b-4)=40`

`color(white)("perimeter ")=2b+10b-8=40`

`"rArr12b-8=40`

`"add 8 to both sides"`

`12bcancel(-8)cancel(+8)=40+8`

`rArr12b=48`

`"divide both sides by 12"`

`(cancel(12) b)/cancel(12)=48/12`

`rArrb=4`

`"and length "=(5xx4)-4=16`

`rArr"area "=16xx4=64" square metres"`

Answer 2

`64m^2`

Explanation:

Let x be the width of the rectangle:

Then the length is 5 times the width minus 4. i.e.

Length = `5x-4`

The perimeter is the sum of all the lengths of the sides. We have:

2 sides that are `5x-4` and 2 sides that are `x`. These add up to `40`, so:

`2(5x-4)+2(x)=40`

Solve for `x`

`10x-8+2x=40`

`12x=48`

`x=48/12=4`

Dimensions of rectangle are:

Width `=x=4`

Length `=5x-4=5(4)-4)=16`

Area of rectangle is:

width x length.

`:.`

`4xx16=64m^2`