Answer:
[tex]\large\boxed{A=240\ cm^2}[/tex]
Step-by-step explanation:
Look at the picture.
The formula of an area of a rhombus:
[tex]A+\dfrac{d_1d_2}{2}[/tex]
d₁, d₂ - diagonals
We have d₁ = 30 cm.
Use the Pythagorean theorem to calculate d₂ = 2x.
[tex]x^2+15^2=17^2[/tex]
[tex]x^2+225=289[/tex] subtract 225 from both sides
[tex]x^2=64\to x=\sqrt{64}\\\\x=8\ cm[/tex]
d₂ = (2)(8) = 16 cm.
Substitute:
[tex]A=\dfrac{(30)(16)}{2}=(30)(8)=240[/tex]
