A rhombus has sides of length 10, and its diagonals differ by 4. What is its area?

Guest May 4, 2020

#1**+1 **

rhombus is made of 4 right triangles with the same area

so using pythagorean theorem on one of the 4:

the sides of the triangle would be d/2 and (d+4)/2 and hypotenuse 10

(d/2)^2 + ((d+4)/2)^2 = 10^2 (solve for d)

1/4 * d^2 + 1/4 * (d+4)^2 = 100

d^2 + (d+4)^2 = 400 (multiplied both sides by 4)

d^2 + d^2 + 8d + 16 = 400

2 * d^2 + 8d + 16 = 400

d^2 + 4d + 8 = 200 (divided both sides by 2)

d^2 + 4d - 192 = 0 (16*12=192)

(d + 16)(d - 12) = 0 (2 answers use the positive one)

d = 12 inches

so d+4 = 16 inches

now we got measure of both diagonals

Area = 1/2 times the product of the diagonals

Area = 1/2 * 12 * 16

Area = 1/2 * 192

Area = 96 inches^2

LuckyDucky May 4, 2020