the perimeter of an isosceles triangle is 32cm.the ratio of the equal side to its base is 3:2. find the area of the triangle.
Answers
Step-by-step explanation:
let base is x cm and one equal side is y cm
x+y+y=32
x+2y=32
y:x=3:2
y/x=3/2
2y=3x
x+2y=32
x+3x=32
4x=32
x=32/4=8
so base is 8 cm and equal sides are (32-8)/2cm
12 cm each
height of the triangle is√(12^2-4^2)cm
=√128cm=8√2cm
Area of the triangle is 1/2.8.8√2sqcm
=32√2sqcm
The perimeter of an issosceles ∆-32 cm.
given that the ratio of the Equal sides to its
base is 3:2
so the ratio of the three sides of the issosceles
∆=3:3:2
sum the ratio 3+3+2=8
length of the Equal sides=3/8×32= 3×4=12
length of the base =2/8×32=2×4=8
according to heron's fromula.area of an
issosceles ∆ with Equal sides a & base b
= 1/4×b×√ (4a2 - B2)
Area of the given issosceles triangle where
a =12 & b =8
1/4×8×√(4×12)-8²
2×√(4×144)-64=2×√576-64
2×√512-2×√2×16×16
2×16×√2=32√2
** m=2