Question

given rhombus and square have equal area and one of diagonal of rhombus is one side of square if length of square is 10 cm find a) diagonals of rhombus if one is half of the othe b)area of square c)area of rhombus d) perimeter of square​

Answer 1

a) 10 cm and 20 cm

b) 100 cm^2

c) 100 cm^2

d) 40 cm

Explanation:

Given:

`a(rhombus) = a(square)`

`l(square) = 10 \: cm`

`diagonal1 = 2 * diagonal2`

Find:

a) Diagonals of the rhombus

We already know the length of one diagonal (which is 10 cm, since it was said, that is is equal to a square's length)

Now, we can find the other one (d2 is the second diagonal):

10 cm = 0,5 × d2 (divide both sides from 0,5)

d2 = 20 cm

b) Area of the square

`a(square) = {l}^(2) = {10}^(2) = 100 \: {cm}^(2)`

c) Area of the rhombus:

`a(rhombus) = (1)/(2) * d1 * d2 = (1)/(2) * 10 * 20 = 100 \: {cm}^(2)`

d) Perimeter of the square (we multiply one side's length by 4, since square has 4 identical sides):

`p(square) = l * 4 = 10 * 4 = 40 \: cm`