Mathematics, 06.04.2020 04:50, itzdulce

Select the three measurements that could be side lengths that form a right triangle
7cm
11cm
54 cm
60 cm
61 cm
65 cm

Answers: 2

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answered: xDoxing

The side lengths of a right triangle is 11cm, 60cm and 61cm, that could be selected from the given measurements.

Step-by-step explanation:

The measurements are,

7cm, 11cm, 54cm, 60cm, 61cm, 65cm

Step:1

To check the right angle triangle, Pythagorean theorem can be used.

For a Pythagorean theorem,

$Side^{2} + Side^{2} = Hypotenuse^{2}$ ..........................(1)

The side values are lower than the hypotenuse,

$c=\sqrt{a^{2}+b^{2} }$ ...................................(2)

Where,

a,b - side values

c - Hypotenuse

For right angle triangle, c > a, b

Alternative : 1

Take, a = 7cm, b = 11cm

From eqn (2),

$c = \sqrt{7^{2}+11^{2} }$ = $\sqrt{170}$ = 13.04

The above value is not equal to the any one of the values of ( 54cm. 60cm, 61cm, 65cm ), So its not an sides of right triangle.

Alternative : 2

Take, a = 7cm, b = 54cm

From eqn (2),

$c = \sqrt{7^{2}+54^{2} }$ = $\sqrt{2965}$ = 54.45

The above value is not equal to the any one of the values of (60cm, 61cm, 65cm ), So its not an sides of right triangle.

Alternative : 3

Take, a = 7cm, b = 60cm

From eqn (2),

$c = \sqrt{7^{2}+60^{2} }$ = $\sqrt{3649}$ = 60.406

The above value is not equal to the any one of the values of (61cm, 65cm ), So its not an sides of right triangle.

Alternative : 4

Take, a = 7cm, b = 61cm

From eqn (2),

$c = \sqrt{7^{2}+61^{2} }$ = $\sqrt{3770}$ = 61.40

The above value is not equal to the values of (65cm ), So its not an sides of right triangle.

Alternative : 5

Take, a = 11cm, b = 54cm

From eqn (2),

$c = \sqrt{11^{2}+54^{2} }$ = $\sqrt{3037}$ = 55.1089

The above value is not equal to the any one of the values of (60cm, 61cm, 65cm ), So its not an sides of right triangle.

Alternative : 6

Take, a = 11cm, b = 60cm

From eqn (2),

$c = \sqrt{11^{2}+60^{2} }$ = $\sqrt{3721}$ = 61

The above value is equal to the values of (61cm ), So its an sides of right triangle. The three sides are 11, 60 and 61.

Step:2

Check for solution,

$11^{2} + 60^{2} = 61^{2}$

3721=3721

Result:

The side lengths of a right triangle is 11cm, 60cm and 61cm, that could be selected from the given measurements.

answered: Guest

It is 7 because it is the absolute value

answered: Guest

.there can be infinite values of m and n that can satisfy the above equation. for each value of m of m or n. there maybe infinite sets of solution for the above

step-by-step explanation:

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Select the three measurements that could be side lengths that form a right triangle
7cm
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