a triangle and a parallelogram stand on the same base of 15 and have the same area. if other sides of the triangle are 30m and 40 metre, find the corresponding height of the parallelogram
Answers
ATQ,
a triangle and a parallelogram stands on the same base of 15m and also have the same area.
other sides of the triangle are 30m and 40m.
here, we've to find the altitude of the parallelogram.
so first of all, we've to find the area of the triangle.
let the sides of the triangle be a, b and c respectively.
semi-perimeter (s) = (15 + 30 + 40)/2
= 85/2
= 42.5m
by using heron's formula, we get
area = √s(s - a)(s - b)(s - c)
= √[42.5(42.5 - 15)(42.5 - 30)(42.5 - 40)]
= √(42.5 × 27.5 × 12.5 × 2.5)
= 191m² (approximately)
therefore area of the parallelogram is also 191m²
now, formula to find the area of a parallelogram is base × height
➡ base × height = 191m²
➡ 15 × height = 191m²
➡ height = 191/15
➡ height = 12.7m (approximately)
hence, the corresponding height of the parallelogram is 12.7cm
: Solution :
By using semi - perimeter :
=(15 + 30 + 40)/2
= 85 / 2
= 42.5 m
Heron's formula for area
= √s ( s - a ) ( s - b ) ( s - c )
=√ [ 42.5( 42.5 - 15)(42.5 - 30)(42.5 - 40)
= √[ 42.5 × 27.5 × 12.5 × 2.5 ]
= 191 m^2
Parallelogram formula for area
=Base × Height
Height = 15/191m^2
Height = 12.7 m