The perimeter of a right angled triangle is 48 centimetres and its area is 96 square centimetres. Length of the hypotenuse is 20 centimetres
a)What is the sum of the lengths of the perpendicular sides?
b) (x+y)² - 4 x y = ______
c)What are the lengths of the perpendicular sides?
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Answer:
hi
purple u ❤️
Step-by-step explanation:
ANSWER
Given: Area =96 cm
2
and Perimieter =48cm
Let a,b,c be the sides of a right triangle, with c as hypotenuse.
Area=
2
1
ab=96
ab=192
b=
a
192
Perimeter=a+b+c=48
c=48−a−b
From Pythagoras Theorem,
c
2
=a
2
+b
2
(48−a−b)
2
=a
2
+b
2
2304+(a+b)
2
−96(a+b)=a
2
+b
2
2304+a
2
+b
2
+2ab−96(a+b)=a
2
+b
2
2304+2ab−96a−96b=0
Divide by 2,
1152+ab−48a−48b=0
1152+a(
a
192
)−48a−48(
a
192
)=0
1344−48a−
a
9216
=0
48a
2
−1344a+9216=0
a
2
−28a+192=0
a=16 and a=12
There are 2 possibilities as we have 2 perpendicular side
If, a=16, b=
a
192
=
16
192
=12
If, a=12, b=
a
192
=
12
192
=16
If, a=12 then b=16 or if b=12 then a=16
It doesn't make a difference while computing c
c
2
=a
2
+b
2
c
2
=144+256=400
c= Hypotenuse =20 cm
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