Find the area of a rectangle if its perimeter is 14 and the ratio of adjacent sides is 2: 5.

To calculate the area of a rectangle, you need to find the product of its two adjacent sides.

Let us denote the sides by the letters X and Y.

Then, according to the condition of the task, we obtain the following relations and the equation of the perimeter.

1) X / Y = 2/5.

2) 2X + 2U = 14.

Let us express X through Y in the 1st ratio.

X = 0.4U.

Now let’s substitute the X value in the 2nd equation.

2 * 0.4U + 2U = 14.

2.8V = 14.

Y = 5.

It remains to calculate the value of X.

X = 0.4 * 5.

X = 2.

So the sides of the rectangle are 2 and 5.

Let’s find their product and calculate the area of the rectangle.

2 * 5 = 10.

Answer: the area of the rectangle is 10.