Question

Suppose the Marshall Islands have an area of about 70 square miles. Suppose a rectangle, with sides x and 2x + 4, has an area of 70 square miles. Find the value of x?

Answer 1

The value of x is 5.

Explanation:

We are given the following in the question:

Area of rectangle = 70 square miles

The sides of the rectangle are:

`w = x, l = (2x+4)`

Area of rectangle =

`A = l* w`

Putting values, we get.

`70 = (2x+4)x\\\Rightarrow 2x^2 + 4x - 70 = 0 \\\Rightarrow 2(x + 7)(x - 5) = 0\\\Rightarrow (x+7) = 0, (x-5) = 0\\\Rightarrow x = -7, x = 5`

Since, the value of x cannot be negative as it represents side of a rectangle.

Thus, the value of x is 5.