Geometry problem, help!!!!!!?

Question

An isosceles triangle has area of 110 ft2. If the base is 14 ft, what is the length of the legs? Round your answer to the nearest tenth.

Answer 1

1/2b*h=A
h=110*2/14=15.7ft
then there will be two right angled triangle correspond to the base
then base will be half for those triangles
b1=7ft
by Pythagoras theorem
side(hypotenuse)=
sqrt(15.7^2+7^2)=17.2
therefore two other sides are
17ft

Answer 2

Umm, I don't know if I'm doing this right, but here goes.

Since it's an isosceles triangle, it can be cut in half from the vertex to the base to make two right triangles, because of the altitude.

SO, when you cut it in half, the base is now 7 instead of 14. Now we're only working with half the triangle because the question only wants to know the length of one side, I think.

So if the area is 110 and you cut the isosceles triangle in half, half the area would be 55.

So you do A = 1/2bh,
And plug in 55 = 1/2(7)h
And you get 15.71428571 = height.

Then you apply the pythagorean theorem.

a^2 + b^2 = c^2

15.71428571^2 + 7^2 = c^

Then you get 17.20287114 which is the length of one leg.

Answer 3

A = 1/2(bh)
110 = 1/2(14)h
220 = 14h
15.71 = h

Draw an isosceles triangle. Straight down the center, draw a line from the top tip to the middle of the base. That makes a right angle, yes? You know that since you are splitting the base in half, each half equals 7 ft. We found that the height is 15.71, so now you can use the pythagorean theorem to find the length of one leg. Since the legs of an isosceles triangle are the same, you'll know both.

a^2 + b^2 = c^2
7^2 + 15.71^2 = c^2
49 + 246.80 = c^2
295.80 = c^2

Use a calculator to find the squareroot of that number to find c.

Answer 4

(a) 0.5 x base x height equals area. We know the area is 110 and the base is 14. So : 0.5 x 14 x height = 110. Solve for height, you get 110/7.

(b) Consider a line from the top of the triangle to the base. That line forms a right triangle. I know one leg of the right triangle is 7 (half the base) and I know the other leg is 110/7 (from part a).

(c) use the pythagorean theorem to determine the length of a side: sqrt((7)^2 + (110/7)^2) = 17.2

Answer 5

Area of a triangle = (1/2)bh
A = 110/2 = 55 considering only one triangle
b = 14/2 = 7
height = h = 2A/b = 2(55)/7 = 110/7
By pythag: 7^2 + h^2 = l^2 where l is the side length
l = sqr[49 + (110/7)^2] = sqr[49 + 110^2/49]
= 7sqr[49^2 + 110^2] = 7sqr[2401 + 12100]
= 7sqr[14501]

Answer 6

First we need to figure out the height of the triangle.
Area = 0.5 * base * height
110 = 0.5 * 14 * height
height = 110/7 = 15.714 feet

Now we use Pythagoras to figure out the length that the question really is asking. It's the hypotenuse of a triangle with leg lengths (0.5*14) and (15.714). (Draw a diagram if you don't see why this is so, the diagram should make it very obvious to you).

7^2 + 15.714^2 = 295.939, which is the square of the missing leg length.
Hence, the leg length is sqrt(295.939), or 17.2 feet.

Answer 7

Area of triangle = 1/2 x base x height. Multiply the area by 2 (= 220 ft^2), and divide by the base, so 220/14 = 15.7ft, to the nearest tenth.

Answer 8

110 = 14h/2 = 7h
h = 110/7
If x is the length of a leg, then:
x^2 = 7^2 + h^2
= 49 + (110/7)^2
= 49 + 246.939
= 295.939
x = sqrt(295.939) = 17.2 to nearest tenth.

Answer 9

Half the base is 7 so height is 110/7.

leg² = base² + height²
leg² = 7² + (110/7)² = 295.9388
leg = 17.20 ft.

Answer 10

I undergo in ideas that there's a thorem that if both aspects of a traingle are equivalent then the perspective opposite to them are also similar. Please see the thorem. So the bisectors make a isoscele traingle with the aspect in between the angles were getting bisected.i will later write you the info of the theorm. because the each and each and every 1/2 of the angles are equivalent, then the completed angles are equivalent. right here you discovered both angles are equivalent. As in step with definition: in a traingle if both angles are equivalent, then that traingle is termed a isoscele traingle.