Mathematics, 26.01.2020 07:31 paulesparsa6

Do you hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg the longer leg is 7 feet longer than the shorter leg find the dimensions of the triangle

Answers: 1

Show answers

Answers

Answer from: ashleydaya

Shorter leg: 8 units

Longer leg: 15 units

Hypotenuse: 17 units

Step-by-step explanation:

We are given h=1+2s where is the hypotenuse and is the length of the shorter leg.

We got this equation from reading that the "hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg". I replaced the "hypotenuse of a triangle" with , "is" with , "1 foot more than" with and finally "twice the length of the shorter leg" with .

We also have "longer leg is 7 feet longer than the shorter leg".

I'm going to replace "longer leg" with .

I'm going to replace "is" with .

I'm going to replace "7 feet longer than the shorter leg" with 7+s .

So we have the equation L=7+s .

So we have a right triangle since something there is a side being referred to as the hypotenuse. We can use Pythagorean Theorem to find a relation between all these sides.

So by Pythagorean Theorem, we have: s^2+L^2=h^2 .

Let's make some substitutions from above:

s^2+(7+s)^2=(1+2s)^2

Let's expand the powers using:

(a+b)^2=a^2+2ab+b^2

Applying this now:

s^2+(49+2(7)s+s^2)=(1+2(1)(2s)+(2s)^2)

s^2+49+14s+s^2=1+4s+4s^2

Combine like terms on right hand side:

2s^2+49+14s=1+4s+4s^2

Subtract everything on left hand side to get 0 on that side:

0=(1-49)+(4s-14s)+(4s^2-2s^2)

Simplify:

0=(-48)+(-10s)+(2s^2)

Reorder into standard form for a quadratic:

0=2s^2-10s-48

Every term is even and therefore divisible by 2. I will divide both sides by 2:

0=s^2-5s-24

I'm going to see if this is factoroable.

We need to see if we can come up with two numbers that multiply -24 and add up to be -5.

Those numbers are -8 and 3.

So the factored form is:

0=(s-8)(s+3)

This implies that either s-8=0 os s+3=0 .

The first equation can be solved by adding 8 on both sides: s=8 .

The second equation can be solved by subtracting 3 on both sides: s=-3 .

The only solution that makes sense for is 8 since it can't the shorter length cannot be a negative number.

s=8

L=7+s=7+8=15

h=1+2s=1+2(8)=1+16=17

So the dimensions of the right triangle are:

Shorter leg: 8 units

Longer leg: 15 units

Hypotenuse: 17 units

Answer from: Quest

step-by-step explanation:

4227473658779875563886538705958641728563470543621287463824132573847969p05749365273847906970680574936214

Iam stuck on this problem and am having trouble solving it. dies anyone know the steps to solving it

Answer from: Quest

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove.

an inaccurate proof leads to errors, or stating results that are not accurate. which wil mess the probelm up you dont want this

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 19:30, JacobWat

He mass of a single atom of carbon can be found by dividing the atomic mass (12.01 g) by 6.022 x 10^23. which is the mass of a single carbon atom, correctly written in scientific notation with the correct number of significant figures?

Answers: 1

continue

Mathematics, 21.06.2019 21:00, Abdullah1860

George is putting trim around his rectangular deck, including the gate. he will need 44 feet of trim to do the entire deck. if the deck is 13 feet long, how wide is the deck?

Answers: 2

continue

Mathematics, 22.06.2019 01:30, chris199825

Agrasshopper weighs 0.89 grams. express the grasshopper’s weight in scientific notation.

Answers: 3

continue

Mathematics, 22.06.2019 02:50, QueenNerdy889

Atourist boat is used for sightseeing in a nearby river. the boat travels 2.4 miles downstream and in the same amount of time, it travels 1.8 miles upstream. if the boat travels at an average speed of 21 miles per hour in the still water, find the current of the river.

Answers: 2

continue

You know the right answer?

Do you hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg the longer l...