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Easy

Question

# Find the area of a rectangular plot, one side of which measures 70 m and the diagonal is 74 m.

## The correct answer is: Area of the given rectangular plot is 1,680 m2

### Hint:-

Area of a rectangle = length * breadth

All angles in a rectangle are equal to 90°

Diagonal of a rectangle divides it into 2 right angled triangles.

Step-by-step solution:-

In the adjacent diagram, we can see that the diagonal divides the given rectangle into 2 right angled triangles.

Also, diagonal of the rectangle becomes the hypotenuse of the 2 triangles.

Hypotenuse of the given triangles = diagonal of the given rectangle = 74m

Now, 1 side of the rectangle = 1 side of the triangle = 70m

Let the other side be x m

By applying Pythagorean theorem, For a right angled triangle-

Hypotenuse2 = sum of the squares of the remaining 2 sides

∴ (74)2 = x2 + (70)2

∴ 5,476 = x2 + 4,900

∴ 5,476 - 4,900 = x2

∴ x2 = 576

∴ x = 24 .............................. (Taking square root both the sides) ........................ (Equation i)

Area of the given plot = length * breadth

∴ Area of the given plot = 70 * 24 ...................................................................................... (From given information & Equation i)

∴ Area of the given plot = 1,680 m2

Final Answer:-

∴ Area of the given rectangular plot is 1,680 m^{2}.

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