Question

The heights of two similar parallelograms are 16 inches and 20 inches. Their

respective areas are (3x+5) square inches and 9x square inches. Find the value of

X?

Answer 1

Answer:
`x=(25)/(21)`

Explanation:

Area of parallelogram = Base x height

If two parallelograms are similar, then their corresponding sides are proportional.

That means,
`\frac{\text{Area of first parallleogram}}{\text{Area of second parallleogram}}=\frac{\text{height of first parallelogram}}{\text{height of second parallelogram}}`

`\Rightarrow (3x+5)/(9x)=(16)/(20)\Rightarrow (3x+5)/(9x)=(4)/(5)\\\\\Rightarrow 5(3x+5)=4(9x)\\\\\Rightarrow\ 15x+25 = 36x\\\\\Rightarrow\ 36x-15x=25\\\\\Rightarrow\ 21x = 25\\\\\Rightarrow\ x=(25)/(21)`

Hence,
`x=(25)/(21)`