Question

Tasha is planning an expansion of a square flower garden in a city park. If each side of the original garden is increased by 7 m, the new total area of the garden will be 144 m2. Find the length of each side of the original garden.

Answer 1

Answer:

The length of the side of the original garden is 5 m.

Step-by-step explanation:

Let the original side of the garden be x.

SInce we are given that the side is incresed by 7 m.

So, the new side = x+7

Formula of area of square = $x^{2}$

Where x is the side length of square .

So, area of garden after increasing the length of side by 7 =$(x+7)^{2}$

Since we are given that the new total area of the garden will be $144m^2$

⇒$(x+7)^{2}=144$

⇒$(x+7)^{2}=12^2$

⇒$x+7=12$

⇒$x=12-7$

⇒$x=5$

Thus the length of the side of the original garden is 5 m.

Answer 2

Since the new and old garden are similar shapes, the length of each side of the original garden would be: 5 meters.

What is the Area of Similar Shapes?

The areas of similar shapes can be compared as a ratio of the square of their sides.

Thus, if a is a side of a shape with A as area, and b with a shape with B is its area, therefore, the ratio of their area would be: A/B = a²/b².

The new and original shapes are similar shapes. Therefore:

side of original garden = x

side of the new garden = x + 7

Area of new garden = 144 sq. m.

Area of the original garden = x²

Thus:

144/x² = (x + 7)²/x²

Cross multiply

(144)(x²) = (x + 7)²(x²)

144 = (x + 7)²

√144 = x + 7

12 = x + 7

12 - 7 = x

x = 5

Therefore, since the new and old garden are similar shapes, the length of each side of the original garden would be: 5 meters.

Learn more about areas of similar shapes on:

https://brainly.com/question/12580764