Question

a rectangular garden measures 5m by 7m. Both dimensions are to be extended by the same amount so that the area of the garden is doubled. by how much should the dimensions increase, to the nearest tenth of a metre?

Answer 1

To double the area of a rectangular garden with dimensions of 5m by 7m, both dimensions should be increased by approximately 1.9 meters.

Step-by-step explanation:

To double the area of a rectangular garden, both dimensions need to be extended by the same amount. Let's call this amount 'x'.

The original dimensions of the garden are 5m by 7m, so the original area is 5m * 7m = 35 square meters.

When we extend both dimensions by 'x', the new dimensions will be (5 + x) meters by (7 + x) meters. The new area will be (5 + x) meters * (7 + x) meters.

We need to find the value of 'x' that makes the new area double the original area. Therefore, we can set up the equation: (5 + x) meters * (7 + x) meters = 2 * 35 square meters.

Simplifying the equation, we get: 35 + 5x + 7x +
`x^2` = 70.

Combining like terms and rearranging, we have:
`x^2` + 12x - 35 = 0.

Using the quadratic formula, we can solve for 'x'. The solutions are approximately -14.9 and 1.9. Since we're looking for a positive value for 'x', the dimensions should increase by approximately 1.9 meters.