The ratio of adjacent sides of a rectangle is 4:5. Find the dimensions of the rectangle if its length is (x+1) cm and the width is (x-3) cm. Hence determine the ratio of the area of the rectangle to its perimeter?

Question

Mathematics

Aurora Patel

4 April, 09:35

The ratio of adjacent sides of a rectangle is 4:5. Find the dimensions of the rectangle if its length is (x+1) cm and the width is (x-3) cm. Hence determine the ratio of the area of the rectangle to its perimeter?

+5

Answers (1)

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Isis Rush · Answer 1

Set an equation:

4/5=x-3/x+1

cross multiply

5x-15=4x+4

x=19

Width: 16 cm

Length: 20 cm

Find the perimeter and the area:

Perimeter: 16+16+20+20=72

Area: 20•16=320

Ratio: 320:72

Simplify the ratio:

40:9

Answer: The ratio of the area to the perimeter is 40:9.