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coldgirl [10]
2 years ago
9

A hockey team is revealing their championship banner outside their stadium. The banner is in the shape of a triangle with a heig

ht that is 4 times as tall as the base length of the banner. If the total area of the banner is 18 square meters (18m2), what is the length of the base of the banner in meters?
Mathematics
1 answer:
kipiarov [429]2 years ago
5 0

Answer: the length of the base of the banner is 3 meters.

Step-by-step explanation:

Assuming the banner is in the shape of a right angle triangle, we would apply the formula for determining the area of a triangle which is expressed as

Area = 1/2 × base × height

Let b represent the base

The banner is in the shape of a triangle with a height that is 4 times as tall as the base length of the banner. It means that the height of the banner is 4b

If the total area of the banner is 18 square meters, it means that

18 = 1/2 × b × 4b

18 = 2b²

b² = 18/2 = 9

b = √9 = 3 meters

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Jimmy's backyard is rectangle that is 18 5/6 yards long and 10 2/5 yards wide Jim buy sod in pieces that are 1 1/3 yard long and
g100num [7]

Answer:

111 pieces of soda

Step-by-step explanation:

step 1

Find the area of the rectangular backyard

The area of the rectangular backyard is equal to

A=LW

where

L=18\frac{5}{6}\ yd=\frac{18*6+5}{6}=\frac{113}{6}\ yd

W=10\frac{2}{5}\ yd=\frac{10*5+2}{5}=\frac{52}{5}\ yd

substitute

A=(\frac{113}{6})(\frac{52}{5})

A=\frac{5,876}{30}\ yd^2

step 2

Find the area of one piece of sod

The area of the rectangular piece of sod is

A=LW

where

L=1\frac{1}{3}\ yd=\frac{1*3+1}{3}=\frac{4}{3}\ yd

W=1\frac{1}{3}\ yd=\frac{1*3+1}{3}=\frac{4}{3}\ yd

substitute

A=(\frac{4}{3})^2\\\\A=\frac{16}{9}\ yd^2

step 3

Find the pieces of sod needed

To find out how many whole pieces of sod will Jim need to buy to cover his backyard, divide the area of the backyard by the area of one piece of soda

so

\frac{5,876}{30} : \frac{16}{9}=\frac{52,884}{480}=110.175

Round up

111 pieces of soda

8 0
3 years ago
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