The length of base of a triangle is 2 cm more than its height. The area is 24 cm². What is the hypotenuse and the perimeter of the triangle?
A. Height=10cm; Perimeter=24cm;
B. Height=24cm; Perimeter=10cm
C. Height =6cm; Perimeter=24cm
D. Height=14cm; Perimeter=24cm
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Answer:
C. Height = 6cm , Perimeter = 24cm
Step-by-step explanation:
Let x be the height of the triangle
Then, the base will be x+2
Area = hb/2
24 = x(x+2)/2
24×2 = x^2 + 2x
x^2 + 2x-48 = 0
x^2+8x-6x+48 = 0
x(x+8)-6(x+8) = 0
(x-6)(x+8) = 0
x-6 = 0 , x+8 = 0
x=6 , x=-8
x is the value of distance so it can't be negative.
Therefore, the value of x is 6 cm.
height = x = 6cm
base = x+2 = 6+2 = 8cm
Hypotenuse = √(6^2 + 8^2)
Hypo. = √(36+64)
= √100
= 10cm
Hypotenuse of the triangle is 10cm.
Perimeter = base+height+hypotenuse
= 8+6+10
= 24 cm
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