one leg of a right triangle has length 7. the lengths of the other two sides are whole numbers. the length of the other leg is ?

Question

vampirchik [111]

2 years ago

15

one leg of a right triangle has length 7. the lengths of the other two sides are whole numbers. the length of the other leg is ?

and the length of the hypotenuse is ?

Mathematics

2 answers:

zalisa [80] · Answer 1 · 2022-04-27T13:18:28+03:00

zalisa [80]2 years ago

4 0

Sets of three integers that could be right triangles are called pythagorean triples. the only pythagorean triple including 7 is 7, 24, and 25. so the length of the other leg is 24 and the length of the hypotenuse is 25. hope this helped!

timama [110] · Answer 2 · 2022-04-27T14:23:17+03:00

Answer:

The length of other leg is 24 units and length of hypotenuse is 25 unit.

Step-by-step explanation:

Given information: In a right angled triangle

Length of one leg = 7 units

In a right angled triangle,

$hypotenuse^2=perpendicular^2+base^2$

If a, b, and c are positive integers, such that

$a^2+b^2=c^2$

then (a,b,c) is known as Pythagorean triple.

The lengths of other two sides are whole numbers. It means the set of sides is a Pythagorean triple.

Pythagorean triple = (3,4,5), (5,12,13), (8,15,17), (7,24,25), (20,21,29)...

Only one Pythagorean triple has 7, i.e, (7,24,25).

Therefore the length of other leg is 24 units and length of hypotenuse is 25 unit.