The are of anisosceles triangle is 48 cm spuare
Ifeach
of the equal sides is 10cm. Find the length
of third side.
Answers
In the given triangle, let the base be x . Here I will use Heron’s formula.
First we need semi-perimeter,
s=a+b+c2
Here s is semi-perimeter, a, b, and c are the 3 sides of triangle.
Therefore,
s=10+10+x2
s=20+x2
Now apply Heron’s formula,
s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√
Putting the values,
20+x2(20+x2−10)(20+x2−10)(20+x2−x)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√
20+x2(x2)(x2)(20−x2)−−−−−−−−−−−−−−−√
Applying (a+b)(a−b)=a2−b2
(202−x2)4(x24−−−−−−−−−√)
(20x)2−x416−−−−−−−√
400x2−x4√4
x2(400−x2)√4
x(400−x2√)4
Now this is the area which is given equal to 48cm2 .
This forms the equation-
x(400−x2√)4=48
x(400−x2−−−−−−−√)=192
Squaring both sides
x2(400−x2)=36864
−x4+400x2=36864
−x4+400x2−36864=0
Here take y=x2 as this became a 4 degree polynomial.
−y2+400y−36864=0
Now factorise
−y2+(256+144)y−36864=0
−y2+256y+144y−36864=0
−y(y−144)+256(y−144)=0
(−y+256)(y−144)=0
Product is 0, so take these both equal to 0.
1. −y+256=0
y1=256
2. y−144=0
y2=144
Earlier we have taken y=x2 , so the values in terms of x are-
x12=256
x1=16
x22=144
x2=12
The base can either be of 12cm or of 16cm , both are correct
PLZ MARK MY ANSWER AS BRAINLIEST
Answer:
9.6
Step-by-step explanation:
area=1/2×b×h
48=1/2×b×h
48=b×10/2
48=b×5
b=48/5
b=9.6
