The perimeter of the triangle will be 56 inches.
The triangle in which one angle is at 90 degrees and the two sides of the triangle are at 90 degrees is called a right-angled triangle. A triangle is a two-dimensional shape having three sides the angle suspended by the triangle is 180 degrees.
Given that the longer leg of a right triangle is three inches more than three times the length of the shorter leg. The area of the triangle is 84 square inches.
The perimeter of the triangle is calculated by knowing the length of all three sides of the triangle;-
Three sides are:-
Shorter side = s
Longer side = 3s + 3
Hypotenuse =?
H = √ ( s² + ( 3s + 3 )²
H = √ ( s² + 9s² +18s + 9 )
H = √ ( 10s² + 18s + 9 )
Form the area the value of s will be calculated as below:-
Area = ( 1 / 2 ) x s x (3s + 3 )
168 = 3s² + 3s
3s² + 3s - 168 = 0
s² + s -56 = 0
s² + 8s - 7s -56 =0
s ( s + 8 ) -7( s+ 8 ) = 0
s = 7 and -8 ignore negative
Three sides are:-
Shorter = s = 7 inches
Longer = 3s + s = 3 x 7 + 3 = 24 inches
Hypotenuse = √ ( 10( 7)² + 18 x (7 ) + 9 )
Hypotenuse = √ ( 490 + 126 + 9 0
Hypotenuse = 25 inches
Perimeter = 7 + 25 + 24 = 56 inches
Therefore, the perimeter of the triangle will be 56 inches.
To know more about a right-angled triangle follow
https://brainly.com/question/64787
#SPJ1