SOLUTION: A public vegetable garden is divided up in different shapes for those who wish to grow vegetables there. Mitch’s piece is in the shape of a right triangle and has an area of 40 s

Question 1152370: A public vegetable garden is divided up in different shapes for those who wish to grow vegetables there. Mitch’s piece is in the shape of a right triangle and has an area of 40 square feet. The longer leg is 6 feet less than twice the shorter leg. What are the lengths of the two legs of that triangle?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A public vegetable garden is divided up in different shapes for those who wish to grow vegetables there.
Mitch’s piece is in the shape of a right triangle and has an area of 40 square feet.
The longer leg is 6 feet less than twice the shorter leg.
What are the lengths of the two legs of that triangle?
:
let x = the length of the shorter leg (let this be the base)
then
(2x-6) = the length of the longer leg (let this be the height)
:
the area
*b*h = 40
b*h = 80
Replace b and h
x(2x-6) = 80
2x^2 - 6x - 80 = 0
simplify, divide by 2
x^2 - 3x - 40 = 0
Factors to
(x-8)(x+5) = 0
the positive solution is what we want here
x = 8 ft is the shorter leg
then
2(8) - 6 = 10 ft is the longer leg
:
:
Check in the area equation
*8*10 = 40
RELATED QUESTIONS
In a neighborhood, 80% of the families have a vegetable garden, and 25% have a vegetable... (answered by ikleyn)

(a) In a random sample of 150 persons having their lunch at the University cafeteria on... (answered by stanbon)

You are visiting your grandparents on their farm. They have asked you to design a small,... (answered by ankor@dixie-net.com)

Caroline has a rectangular vegetable garden that measures 4 m x 6 m . she wants to... (answered by fractalier)

A pizza parlor has 6 meat options, 8 vegetable options, 3 sauces, and 4 types of cheese. (answered by math_tutor2020)

A gardener has six rows available in his vegetable garden to place tomatoes, eggplants,... (answered by ikleyn)

To make a 15ft by 20ft section of a yard into a garden. They plant flowers in 2/3 of the... (answered by jorel1380)

A small farm has 70 acres of space to plant. The farmer wants to grow corn and green... (answered by ankor@dixie-net.com)

It is lunchtime and you wish to build a pizza with 1 choice of crust, 1 meat, 1... (answered by Fombitz)