for the first question:
Which of these sets could represent the side lengths of a right triangle?
{4, 8, 12}
{6, 8, 10}
{6, 8, 15}
{5, 7, 13}
you must use pythagorean theorem to find the answer: a²+b²=c²
so in this case 4²+8² should equal 12²
4²=16
8²=64
12²=144
if 4²+8² should equal 12² then 16+64 should equal 144 but it does not
16+64=80 therefore the first option is not a right triangle.
{6, 8, 10}
6²+8² should equal 10²
6²=36
8²=64
10²=100
36+64=100
therefore...this is the correct answer. i'll do the other options to prove that this is correct though.
{6, 8, 15} we know this is wrong because we just found that 6²+8² is equal to 10²
how could it equal both 10² AND 15²? it can't
{5, 7, 13}
5²=25
7²=49
13²=169
25+49=74
this is wrong
{6, 8, 10} is the answer
Question 31:
At the electronics store, television screens are sized by the lengths of their diagonals. The television that Mrs. Mallory wants to buy has a 25 inch diagonal. The width of the screen is 15 inches. What is the height of the screen?
If you were cut a rectangle in half from corner to corner, you would have two triangles. The hypotenuse is the diagonal line that you cut, which is 25in²
and the width of the triangle is 15in²
25²-15²=400
25²=625
15²=225
625-225=400
25²-15²=400
square root of 400=20
how do we know if 20 inches is correct? we add
20²+15²=
20²=400
15²=225
400+225=625
20²+15²=25²! therefore the equation is correct!
20 inches is the answer
Question 41
Determine the missing length. Round to the nearest foot.
320²+340²=c²
320²=102,400
340²=115,600
102,400 + 115,600= 218,000
square root of 218,000=466.9
rounded to nearest foot is 467