Mathematics, 18.07.2019 13:30 dontcareanyonemo

An isosceles triangle has an area of 125 feet. if the base is 14 feet, what is the length of each leg

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Answer from: dnee8321

Area of a right triangle is (1/2) x base x height
Cut the isosceles triangle in half to create a 90° triangle.
Then, (1/2)Area = (1/2) base x height
   (1/2)(125) = (1/2) (14/2) x height
      125 = 7 x    h
125/7 = h

Now use Pythagorean Theorem to find the hypotenuse (c):
a² + b² = c²
(7)² + (125/7)² = c²
49 + 318.88 = c²
367.88 = c²
   19.18 = c
Since it is an isosceles triangle, the legs are the same length.

the length of each leg is ≈ 19.18

Answer from: mia53408

Look at the picture.
The formula of the area of a triangle is: $A_\Delta=\dfrac{1}{2}bh$
$b=14\ ft.;\ A_\Delta=125\ ft.$
substitute:
$\dfrac{1}{2}\cdot14\cdot h=125\\\\7h=125\ \ \ |:7\\\\h=\dfrac{125}{7}\ ft.$

Use the Pythagorean theorem
$l^2=\left(\dfrac{14}{2}\right)^2+\left(\dfrac{125}{7}\right)^2\\\\l^2=7^2+\dfrac{15625}{49}\\\\l^2=49+\dfrac{15625}{49}\\\\l^2=\dfrac{2401}{49}+\dfrac{15625}{49}\\\\l^2=\dfrac{18026}{49}\\\\l=\sqrt{\dfrac{18026}{49}}\\\\l=\dfrac{\sqrt{18026}}{7}\approx19.18\ ft.$

An isosceles triangle has an area of 125 feet. if the base is 14 feet, what is the length of each le

An isosceles triangle has an area of 125 feet. if the base is 14 feet, what is the length of each le

Answer from: Quest

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

Answer from: Quest

total of apples - take away four

6-4 = 2

answer is 2 apples

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