Question

The perimeter of rectangle MNPQ is 80 in and the ratio MN : MQ = 3:5. Find the area of MNPQ

Answer 1

The area of MNPQ is 375 square inches.

Explanation:

It is given that the ratio MN : MQ = 3:5. It means the ratio of dimensions is 3:5.

Let the dimensions of the rectangle be 3x by 5x.

The perimeter of a rectangle is

`P=2(length+width)`

It is given that the perimeter of rectangle MNPQ is 80.

`80=2(3x+5x)`

`80=2(8x)`

`80=16x`

Divide both sides by 16.

`5=x`

The value of x is 5.

The dimensions of the rectangle are 15 and 25.

The area of rectangle is

`A=length* breadth`

`A=15* 25`

`A=375`

Therefore the area of MNPQ is 375 square inches.

Answer 2

Let's write 3:5 = 3k:5k. Then using perimeter formula, we can write that
`P=(3k+5k)2=80` and k=5 cm. The sides are 15 cm and 25 cm. The area is
`A=15*25=375 cm^(2)`