A piece of wire 40cm long is bent to form a right-angle whole hypotenuse is 17cm long.Find the length of each of the other two sides.

      

A piece of wire 40 cm long is bent to form a right-angle whole hypotenuse is 17 cm long.Find the length of each of the other two sides.

  

Answers


Patrick
perimeter of the triangle,P=40cm
Hypotenuse, c=17cm

other sides, b+h=40-17

b+h=23..............(1)
using pythagoras theorem,
b^2 + h^2 = 23^2..........(2)

from eqn (1), b=23-h

subtituting equation b in eqn (2)

(23-h)^2 + h^2 = 17^2

23(23-h)-h(23-h) + h^2 = 289

529-46h+2h^2 = 289

240-46h+2h^2=0

120-23h+h^2=0....................(3)

Solving equation (3) quadratically,

value of h=15

thus 15+b=23
b=8
Therefore the sides are 15cm and 8cm.







Teacher Robin answered the question on February 19, 2018 at 11:41


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