Respuesta :
Given:
a.) The longer leg of a right triangle is 7 cm longer than the shorter leg.
b.) The hypotenuse is 9cm longer than the shorter leg.
Let,
a = length of the longer leg
b = length of the shorter leg
c = length of the hypotenuse
We get,
Equation 1:
a = b + 7
c = b + 9
Since it's been mentioned that the figure is a right triangle, we will be using the Pythagorean Theorem in getting the measure of the sides.
[tex]\text{ a}^2+b^2=c^2[/tex][tex]\text{ (b + 7)}^2+b^2=(b+9)^2[/tex][tex]\text{ b}^2+14b+49+b^2=b^2\text{ + 18b + 81}[/tex][tex]\text{ 2b}^2+14b+49\text{ - }b^2\text{ - 18b - 81 = 0}[/tex][tex]\text{ b}^2\text{ - 4b - 32 = 0}[/tex][tex]\mleft(b^2+4b\mright)+\mleft(-8b-32\mright)\text{ = 0}[/tex][tex]b\mleft(b+4\mright)-8\mleft(b+4\mright)\text{ = 0}[/tex][tex]\mleft(b+4\mright)\mleft(b-8\mright)\text{ = 0}[/tex]Therefore,
b = -4 (b + 4)
b = 8 (b - 8)
Since a length is never a negative value, we can therefore conclude that the measure of the shorter leg is 8 cm.
ANSWER:
Longer leg = shorter leg + 7 = 8 + 7 = 15 cm
Hypotenuse = shorter leg + 9 = 8 + 9 = 17 cm
Shorter leg = 8 cm
