The area of a rhombus is 140 square inches; given a diagonal length of 20 inches, how to find its side length?

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nagged

There are a number of ways to do this. Heron’s formula sounds nice since it’ll prevent me from having to deal with angles.

The area of a triangle with side lengths a, b, and c is

A = 1/4 sqrt( [a^2+b^2+c^2]^2 – 2[a^4+b^4+c^4] )

Here, we have a=b and c=20. We may also double this area to find the area of the rhombus, setting A=140 and replacing the 1/4 with 1/2. That is,

140 = 1/2 sqrt( [2a^2 + 20^2]^2 – 2[2a^4 + 20^4] )

This is just a quadratic equation. Solving it gives a=sqrt(149) inches.

perksofbeingawallflower

area = d1d2 / 2

140 = 20*d2 / 2

280 = 20 * d2

14 = d2

area = 140

d1 = 20

d2 = 14

To calculate the side use the pythagorean theorem.

(d1/2)^2 + (d2/2)^2 = C^2

100 + 49 = c^2

sqrt(149) = c

all sides are the same length of c.

ryssee

area =( d1 x d2) /2

140 = (20 x d1)/ 2

d1 = 14

so now we know the sizes of both diagonals which i are d1 = 14. d2 = 20

to find the lenth , we have to devide diagonals in to half, { 7, 10}

L^2 = 7^2 + 10^2

L^2 = 49 + 100

L = 149 UNDER ROOTS

L = 12.2 INCHES

AS WELL WE KNOW ALL THE SIDES OF A ROMBUS ARE EQUAL

over2u

1/2*d1*d2 = 140

d1*d2 = 280

d2 = 280/20

= 14

4*s^2 = d1^2 + d2^2

s^2 = (20^2 + 14^2)/4

= 596/4

= 149

s = 12.21 cm