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lesya [120]
3 years ago
14

The hypotenuse of a right triangle is 10 ft long. the shorter leg is 2ft shorter than the longer leg. find the side lengths of t

he triangle
Mathematics
1 answer:
Gwar [14]3 years ago
5 0
Since we have two possible pieces of information and 2 items to solve for, we know this is a system of equations.
Our first piece of information is that our shorter leg (s) is 2 feet shorter than our longer leg (l). This can be written as s=l-2.
Our second piece of information is that using the Pythagorean theorem that our shorter leg squared plus our longer leg squared is equal to our hypotenuse squared. This can be represented by s^2+l^2=10^2. Now we can solve.
We have already isolated for s in our first equation, so we can substitute l-2 in.
(l-2)^2+l^2=10^2
l-2+l=10
2l-2=10
2l=12
l=6
Now we can substitute in for s in our simpler equation
s=6-2
s=4
We now know that using our knowledge of systems of equations, the side lengths of this right angle triangle are 6 and 4.
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Find the surface area of the figure?
motikmotik

Step-by-step explanation:

the surface area consists of 6 individual areas :

front and back (both are equal)

left and right (both are equal)

top and bottom

front and back are trapezoids.

the area of a trapezoid is

(base 1 + base 2)/2 × h

the bases are the 2 parallel sides.

in our case the area of one trapezoid is

(5 + 19)/2 × 12.1 = 145.2 ft²

front and back together then are 290.4 ft².

left and right are 8×14 rectangles:

8×14 = 112 ft²

together they are 224 ft².

the bottom is a 5×8 rectangle :

5×8 = 40 ft²

the top is a 19×8 rectangle :

19×8 = 152 ft²

so, the total surface area is

290.4 + 224 + 40 + 152 = 706.4 ft²

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2 years ago
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This is writing an expression for the perimeter! Explain how you got your answer.
Kisachek [45]
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3 0
3 years ago
The sum of the ages of two people is 32. The difference is their ages is 4. What is the age of the younger person ?
Gala2k [10]
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5 0
3 years ago
Read 2 more answers
HEY GUYS I NEED THIS ANSWER NOW
Sergio [31]

Let

x-------> the number of fiction books

y-------> the number of nonfiction books.

we know that

x+y=26 -----> equation 1

x=y+12

x-y=12 -----> equation 2

Add equation 1 and equation 2

x+y=26\\x-y=12\\ ------\\ 2x=38\\ x=38/2\\x=19\ fiction\ books

<u>find the value of y</u>

x+y=26

19+y=26

y=26-19=7\ nonfiction\ books

therefore

<u>the answer is</u>

Part a)  the number of fiction books is 19\ fiction\ books

Part b)  the number of nonfiction books is 7\ nonfiction\ books

6 0
3 years ago
Read 2 more answers
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