The four sides of a quadrilateral are in the ratio of 4: 5: 6:7 and its perimeter is 176 cm. Find the length of its longest side.

The ratio of the sides of the quadrilateral = 4:5:6:7

Perimeter of the quadrilateral = 176 cm

The sum of the ratios is equal to the total ratio value, and the actual lengths of the sides are proportional to these ratios. The perimeter of the quadrilateral is the sum of the lengths of all four sides.

Let the common multiplier for the sides be x.

The sides of the quadrilateral;

Sides = 4x, 5x, 6x, 7x

The sum of the sides (i.e., the perimeter) is:

4x + 5x + 6x + 7x = 176

22x = 176

x =$$\frac{176}{22}$$​ = 8

Thus, The longest side corresponds to the ratio 7, so:

Longest side = 7x = 7 × 8 = 56 cm