Q21 of 46 Page 1

The diagonal of a rectangular field is 16 meters more than the shorter side. If the longer side is 14 meters more than the shorter side, then find the lengths of the sides of the field.


Let the shortest side be x


Length of diagonal = x + 16


Length of longer side = x + 14


As this triangle is a right angled triangle it should verify the phythagoras theorem


i.e. (hypotenuse)2 = (base)2 + (perpendicular)2


(x + 16)2 = (x + 14)2 + x2


x2 + 32x + 256 = x2 + 196 + 28x + x2


x2 - 4x - 60 = 0


x2 - 10x + 6x - 60 = 0


x(x - 10) + 6(x - 10) = 0


(x + 6)(x - 10) = 0


x = - 6 [ not possible as length of a side can't be negative ]


or x = 10


so length of longer side of field, x + 14 = 10 + 14 = 24 m


length of shorter side, x = 10 m


More from this chapter

All 46 →
19

A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting total surface area of the solid so formed, at the rate of rs. 5 per 100 sq. cm. (use π = 3.14)

 20

504 cones, each of diameter 3.5 cm and height of 3 cm, are melted and recast into a metallic sphere.

Find the diameter of the sphere and hence find its surface area. (Use π = 22/7)

 22

Find the 60th term of the AP 8, 10, 12, …., if it has a total of 60 terms and hence find the sum of its last 10 terms.

 23

A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If the takes 3 hours to complete the total journey, what is its first speed?