Rhombus - ratio

In a rhombus, the ratio of a side to the height drawn to that side is 4:1, and its area is 49 cm². Calculate the length of the side and the height drawn to that side.

Final Answer:

a =  14 cm
h =  3.5 cm

Step-by-step explanation:

$$\begin{gathered} a:h=4:1 \\ S=49{\text{cm}}^2 \\ a=4h \\ S=a\cdot h \\ S=a\cdot h \\ S=4h\cdot h \\ S=4h^2 \\ h=\sqrt{S/4}=\sqrt{49/4}=\frac{7}{2}=3.5\text{cm} \\ a=4\cdot h=4\cdot 3.5=14=14\text{cm} \\ \text{ Verifying Solution: } \\ {S}_2=a\cdot h=14\cdot 3.5=49{\text{cm}}^2 \end{gathered}$$

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