lizabee2001
lizabee2001 lizabee2001
  • 02-04-2020
  • Mathematics
contestada

A right triangle has the leg lengths of 3X and 40 and a hypotenuse of length 5X. How long are the sides?

Respuesta :

Hrishii
Hrishii Hrishii
  • 02-04-2020

Answer:

Hypotenuse = 10 units

Step-by-step explanation:

According to the Pythagoras theorem:

[tex] {hyp}^{2} = {(one \: leg) }^{2} + {(other \: leg)}^{2} \\ \therefore \: {(5x)}^{2} = {(3x)}^{2} + {40}^{2} \\ \therefore \: {25x}^{2} = {9x}^{2} + 1600 \\ \therefore \: {25x}^{2} - {9x}^{2}= 1600 \\ \therefore \: {16x}^{2}= 1600 \\ \therefore \: {x}^{2}= \frac{1600}{16} \\ \therefore \: {x}^{2}= 100 \\ \therefore \: {x}= 10 \\ [/tex]

Hence, length of hypotenuse = 10 units.

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