Question

The lengths of the two altitudes of a paralleogram is 4cm ,6 cm perimeter is 40 cm find the length of the sides of paralleogram

Answer 1

he sides are 2 parallel sides of 8 cm length and 2 parallel sides of 12 cm length.

step by step Explanation:

Assume that the parallelogram is formed by two vectors, →a, and →b.

Given:

p=2∣∣→a∣∣+2∣∣∣→b∣∣∣=40 cm [1]

The height where →b is chosen to be the base

ha=∣∣→a∣∣sin(θ)=4 cm [2]

where θ is the acute angle between →a and →b

The property, adjacent angles of a parallelogram are supplementary, causes the equation for the height when →a is chosen to be the base to become:

hb=∣∣∣→b∣∣∣sin(π−θ)=6 cm [3]

You can use the identity sin(A−B)=sin(A)cos(B)−cos(A)sin(B) to prove that sin(π−θ)=sin(θ):

hb=∣∣∣→b∣∣∣sin(θ)=6 cm [3.1]

Divide equation [2] by equation [3.1]:

∣∣→a∣∣