Question

Can someone help me with this problem? Thank you!

Answer 1

`\qquad\qquad\huge\underline{{\sf Answer}}`

Since, the Area of smaller rectangle is 35,

• width = 5 ft

Let's calculate it's length ~

`\qquad \sf  \dashrightarrow \:a = l \cdot w`

`\qquad \sf  \dashrightarrow \:35 = l \cdot5`

`\qquad \sf  \dashrightarrow \:l = 35 / 5`

`\qquad \sf  \dashrightarrow \:l = 7 \: ft`

And the two rectangles are similar ~ so the ratio of their sides are equal as well ~

Assume length of greater rectangle be x

`\qquad \sf  \dashrightarrow \: (25)/(5) = (x)/(7)`

`\qquad \sf  \dashrightarrow \:x = 5 * 7`

`\qquad \sf  \dashrightarrow \:x = 35`

Now, since the length and width of the greater rectangle is known, let's find it's Area ~

`\qquad \sf  \dashrightarrow \:a = l \cdot w`

`\qquad \sf  \dashrightarrow \:a = 35 \sdot25`

`\qquad \sf  \dashrightarrow \:a = 875 \: \: ft {}^(2)`

So, Area of the greater rectangle is 875 ft²