Question

The figure below shows a tent with wires attached to help stabilize it. The length of each wire is 8 feet greater than the distance from the ground to where it is attached to the tent. The distance from the base of the tent to where the wire is anchored exceeds this height by 7 feet. Find the length of each wire used to stabilize the tent. Explain your answer in the context of the problem. Hint: Use the Pythagorean Theorem to help you get started. Tent

Answer 1

Answer:

The length of 2 wires are 13 feet and 12 feet [i don't know if the 3rd side is a wire, if so, the length is 5 feet]

Step-by-step explanation:

The image of the tent is attached.

As we can see, it creates a right triangle with "x+8" side being the hypotenuse of the triangle.

The pythagorean theorem tells us:

Hypotenuse^2 = Leg^2 + Leg^2

THe hypotenuse is "x+8", the two legs are "x" and "x+7" respectively. Let's solve for x:

$(x+8)^2=(x+7)^2+x^2$

We expand and solve for x:

$(x+8)^2=(x+7)^2+x^2\\x^2+16x+64=x^2+14x+49+x^2\\x^2+16x+64=2x^2+14x+49\\x^2-2x-15=0\\(x-5)(x+3)=0\\x=5,-3$

Length can't be negative, so x = 5.

Hence, the 3 sides of the triangle are:

x = 5

x + 8 = 13

x + 7 = 12

The length of 2 wires are 13 feet and 12 feet