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

hi,

3. 12.15, you are correct.

4.2.01, your first digit is correct,

hope this !

Hi everyone can you told me answer of number 3 and 4

Answer from: Quest

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.