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:

Answer from: Quest

answer: $201

step-by-step explanation: to get the answer, you first get 3 nieces that he sold and multiply it by 67 and get $201, so he earned $201 selling his nieces.

Another question on Mathematics

Mathematics, 21.06.2019 16:00

Write two subtraction equations that are equivalent to 5 + 12 = 17.

Answers: 2

Answer

Mathematics, 21.06.2019 19:30

The length of a shadow of the building is 36m. the length of the pole, which is perpendicular to the ground, is 1.9m. the length of the pole's shadow is 1.52m. what is the height of the building?

Answers: 1

Answer

Mathematics, 21.06.2019 22:20

1. 2. ∠b and ∠y are right angles. 3.? 4.? which two statements are missing in steps 3 and 4? ∠x ≅ ∠c △abc ~ △zyx by the sas similarity theorem. ∠b ≅ ∠y △abc ~ △zyx by the sas similarity theorem. = 2 △abc ~ △zyx by the sss similarity theorem. = 2 △abc ~ △zyx by the sss similarity theorem.

Answers: 2

Answer

Mathematics, 22.06.2019 00:00

How many quarts of a 50% solution of acid must be added to 20 quarts of a 20% solution of acid in order to get a 40% solution of acid?

Answers: 2

Answer

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...

Questions

Mathematics, 25.09.2019 19:00

In the diagram below. ab is parallel to cd. what is the value of x

Mathematics, 25.09.2019 19:00