Mathematics, 28.06.2019 02:20 linnybear300

The shorter leg of a right triangle is 7ft shorter than the longer leg. the hypotenuse is 7ft longer than the longer leg. find the side lengths of the triangle

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Answer from: ZBSJ

Hello!

The answers are:

$Hypothenuse=28ft+7ft=35ft\\LongerLeg=28ft\\ShorterLeg=28ft-7ft=21ft$

Why?

Since we are working with a right triangle, we can use the Pythagorean Theorem, which states that:

$Hypothenuse^{2}=a^{2}+b^{2}$

Then, we are given the following information:

Let be "a" the shorter leg and "b" the the longer leg of the right triangle, so:

$(7ft+b)^{2}=(b-7)^{2}+b^{2}$

We can see that we need to perform the notable product, so:

$(7ft+b)^{2}=(b-7ft)^{2}+b^{2}\\\\7ft*7ft+2*7ft*b+b^{2}=b^{2}-2*7ft*b+7ft*7ft+b^{2}\\\\49ft^{2} +14ft*b+b^{2}=b^{2}-14ft*b+49ft^{2}+b^{2}\\\\49ft^{2} +14ft*b+b^{2}=-14ft*b+49ft^{2}+2b^{2}\\\\-14ft*b+49ft^{2}+2b^{2}-(49ft^{2} +14ft*b+b^{2})=0\\\\-28ft*b+b^{2}=0\\\\b(-28ft+b)=0$

We have that the obtained equation will be equal to 0 if: b is equal to 0 or b is equal to 28:

0(-28+0)=0

28(-28+28)=28(0)=0

So, since we are looking for the side of a leg, the result that we need its 28 feet.

Hence, we have that the answers are:

$Hypothenuse=28ft+7ft=35ft\\LongerLeg=28ft\\ShorterLeg=28ft-7ft=21ft$

Have a nice day!

Answer from: scoutrussel4life

Base = 21 ft

Height = 28 ft

Hypotenuse = 35 ft

Step-by-step explanation:

It is given that,the shorter leg of a right triangle is 7ft shorter than the longer leg. The hypotenuse is 7ft longer than the longer leg

Let longer leg = x then shorter leg = x - 7 and hypotenuse = x+ 7

To find the side lengths of triangle

Here Base = x-7

Height = x

Hypotenuse = x + 7

By using Pythagorean theorem we can write,

Base² + height² = Hypotenuse²

(x - 7)² + x² = (x + 7)²

x² -14x + 49 + x² = x² +14x + 49

x² - 14x = 14x

x² - 28x = 0

x(x - 28) = 0

x = 0 or x = 28

Therefore the value of x = 28

Base = x - 7 = 21

Height = 28

Hypotenuse = 28 + 7 = 35

Answer from: Quest

$w\geq 14$

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

$2l+2w\geq 40$

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

$2\times 6+2w\geq 40$

now, we can solve for w

$12+2w\geq 40$

subtract both sides by 12

$12+2w-12\geq 40-12$

$2w\geq 28$

divide both sides by 2

and we get

$w\geq 14$

so,

the smallest possible measurement of the width is 14 feet

Answer from: Quest

step-by-step explanation:

what are the statements? and what do you mean by "216 2 1 6"?

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