Explanation:
when given a ratio like this 4:7, it means that one item represents 4 units, and the other 7 units.
let's assume that length is larger than width, so the given 31.5 in are these 7 units.
that means 1 ratio unit is
31.5 / 7 = 4.5 in
the width is 4 units, therefore
width = 4×4.5 = 18 in
the perimeter is
2×length + 2×width = 2×31.5 + 2×18 = 63 + 36 = 99 in
the area is
length × width = 31.5×18 = 567 in²