Which three lengths could be the lengths

Mathematics

1 answer:

Fed [463]3 years ago

6 0

Given:

The three lengths in the options.

To find:

Which three lengths could be the lengths of the sides of a triangle?

Solution:

If the sum of two smaller sides is greater than the largest side, then the three sides can form a triangle otherwise the triangle is not possible.

In option A, the three sides are 4 cm, 8 cm, 13 cm. Here, the largest side is 13 cm.

Sum of two smaller sides is:

$4+8=12$

$4+8$

So, the triangle is not possible.

In option B, the three sides are 13 cm, 11 cm, 23 cm. Here, the largest side is 23 cm.

Sum of two smaller sides is:

$13+11=24$

$13+11>23$

So, the triangle is possible.

In option C, the three sides are 5 cm, 18 cm, 12 cm. Here, the largest side is 18 cm.

Sum of two smaller sides is:

$5+12=17$

$5+12$

So, the triangle is not possible.

In option D, the three sides are 25 cm, 8 cm, 16 cm. Here, the largest side is 25 cm.

Sum of two smaller sides is:

$8+16=24$

$8+16$

So, the triangle is not possible.

Therefore, the correct option is B. The three lengths 13 cm, 11 cm, 23 cm could be the lengths of the sides of a triangle.

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A square rug covers 79 square feet of floor. What is the approximate length of one side of the rug? (Approximate to the nearest

GaryK [48]

Answer:

8.88 feet

Step-by-step explanation: Since it is a square all the sides equal the same number. You may not know how to use square roots yet but, I will show you how they are helpful. The square root of a number is when the 2 numbers being multiplied together are the same. For example, 3*3 is 9. The square root of 9 is 3 because when you multiply 3 and 3 together you get 9. For your problem since all the problems start with 8.8 we know it is bigger than 8 and less than 9 because the square root of 8 is 64 and the square root of 9 is 81. Since 79 is closer to 81 then it is to 64 we know 8.86 and 8.87 won't work because they are too small. From here the best way to figure it out is by trial and error if you are not allowed to use a calculator. So try 8.88 times 8.88 and 8.89 times 8.89. But if you are allowed to use a calculator (a scientific calculator) type in 79. There should be a button that looks like $\sqrt{x\\$ . If you press it it will give you the square root of 79 (which is what you are looking for).