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My name is Ann [436]
2 years ago
9

A square building with an area of 225 m2 has a garden surrounding it that has an equal width on all sides. The area of the garde

n is 1/3 of the area of the building. What is the width of the garden?

Mathematics
1 answer:
xenn [34]2 years ago
8 0

Answer:

The width of the garden is 1.16 m

Step-by-step explanation:

step 1

<em>Find the area of the garden</em>

To find out the area of the garden multiply by 1/3 the area of the building

225(\frac{1}{3})=75\ m^2

step 2

Find the length side of the square building

The area of a square is

A=b^2

where

b is the length side of the square

we have

A=225\ m^2

so

b^2=225\\b=15\ m

step 3

Find the width of the garden

Let

x ----> the width of the garden

we know that

The area of the building plus the area of the garden is equal to

(15+2x)^2=225+75

solve for x

225+60x+4x^2=225+75\\4x^2+60x-75=0

Solve the quadratic equation by graphing

using a graphing tool

The  solution is x=1.16 m

see the attached figure

therefore

The width of the garden is 1.16 m

Find the exact value

The formula to solve a quadratic equation of the form ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

4x^2+60x-75=0  

so

a=4\\b=60\\c=-75

substitute in the formula

x=\frac{-60\pm\sqrt{60^{2}-4(4)(-75)}} {2(4)}

x=\frac{-60\pm\sqrt{4,800}} {8}

x=\frac{-60\pm40\sqrt{3}} {8}

x=\frac{-60+40\sqrt{3}} {8}\ m  ----> exact value

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